# A melhor ferramenta para a sua pesquisa, trabalho e TCC!

Página 1 dos resultados de 29229 itens digitais encontrados em 0.036 segundos

## Dynamic Logics of Dynamical Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/05/2012
Português

Relevância na Pesquisa

67.224854%

#Computer Science - Logic in Computer Science#Mathematics - Dynamical Systems#Mathematics - Logic#03B70, 03B45, 03F03, 68Q60, 34A38, 68M14, 34C45, 37H10, 60H10, 03D78#F.3.1#F.4.1#D.2.4#C.1.m#G.1.4#C.2.4#D.4.7

We survey dynamic logics for specifying and verifying properties of dynamical
systems, including hybrid systems, distributed hybrid systems, and stochastic
hybrid systems. A dynamic logic is a first-order modal logic with a pair of
parametrized modal operators for each dynamical system to express necessary or
possible properties of their transition behavior. Due to their full basis of
first-order modal logic operators, dynamic logics can express a rich variety of
system properties, including safety, controllability, reactivity, liveness, and
quantified parametrized properties, even about relations between multiple
dynamical systems. In this survey, we focus on some of the representatives of
the family of differential dynamic logics, which share the ability to express
properties of dynamical systems having continuous dynamics described by various
forms of differential equations.
We explain the dynamical system models, dynamic logics of dynamical systems,
their semantics, their axiomatizations, and proof calculi for proving logical
formulas about these dynamical systems. We study differential invariants, i.e.,
induction principles for differential equations. We survey theoretical results,
including soundness and completeness and deductive power. Differential dynamic
logics have been implemented in automatic and interactive theorem provers and
have been used successfully to verify safety-critical applications in
automotive...

Link permanente para citações:

## Toric dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.08657%

Toric dynamical systems are known as complex balancing mass action systems in
the mathematical chemistry literature, where many of their remarkable
properties have been established. They include as special cases all deficiency
zero systems and all detailed balancing systems. One feature is that the steady
state locus of a toric dynamical system is a toric variety, which has a unique
point within each invariant polyhedron. We develop the basic theory of toric
dynamical systems in the context of computational algebraic geometry and show
that the associated moduli space is also a toric variety. It is conjectured
that the complex balancing state is a global attractor. We prove this for
detailed balancing systems whose invariant polyhedron is two-dimensional and
bounded.; Comment: We include the proof of our Conjecture 5 (now Lemma 5) and add some
references

Link permanente para citações:

## Non uniformly hyperbolic dynamics: H\'enon maps and related dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/04/2003
Português

Relevância na Pesquisa

67.122246%

In the 1960s and 1970s a large part of the theory of dynamical systems
concerned the case of uniformly hyperbolic or Axiom A dynamical system and
abstract ergodic theory of smooth dynamical systems. However since around 1980
an emphasize has been on concrete examples of one-dimensional dynamical systems
with abundance of chaotic behavior (Collet &Eckmann and Jakobson). New proofs
of Jakobson's one-dimensional results were given by Benedicks and Carleson
\cite{BC85} and were considerably extended to apply to the case of H\'enon maps
by the same authors \cite{BC91}. Since then there has been a considerable
development of these techniques and the methods have been extended to the
ergodic theory and also to other dynamical systems (work by Viana, Young,
Benedicks and many others). In the cases when it applies one can now say that
this theory is now almost as complete as the Axiom A theory.

Link permanente para citações:

## Modular dynamical systems on networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/03/2013
Português

Relevância na Pesquisa

67.1582%

#Mathematics - Dynamical Systems#Physics - Physics and Society#Quantitative Biology - Molecular Networks#Quantitative Biology - Neurons and Cognition

We propose a new framework for the study of continuous time dynamical systems
on networks. We view such dynamical systems as collections of interacting
control systems. We show that a class of maps between graphs called graph
fibrations give rise to maps between dynamical systems on networks. This allows
us to produce conjugacy between dynamical systems out of combinatorial data. In
particular we show that surjective graph fibrations lead to synchrony subspaces
in networks. The injective graph fibrations, on the other hand, give rise to
surjective maps from large dynamical systems to smaller ones. One can view
these surjections as a kind of "fast/slow" variable decompositions or as
"abstractions" in the computer science sense of the word.; Comment: 37 pages. Major revision of arXiv:1008.5359 [math.DS]. Following
referees' suggestions we made the paper more accessible for applied
dynamicists

Link permanente para citações:

## Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/10/2015
Português

Relevância na Pesquisa

67.111577%

In this work, we explore finite-dimensional linear representations of
nonlinear dynamical systems by restricting the Koopman operator to a subspace
spanned by specially chosen observable functions. The Koopman operator is an
infinite-dimensional linear operator that evolves observable functions on the
state-space of a dynamical system [Koopman 1931, PNAS]. Dominant terms in the
Koopman expansion are typically computed using dynamic mode decomposition
(DMD). DMD uses linear observations of the state variables, and it has recently
been shown that this may be too restrictive for nonlinear systems [Williams et
al. 2015, JNLS]. It remains an open challenge how to choose the right nonlinear
observable functions to form a subspace where it is possible to obtain
efficient linear reduced-order models.
Here, we investigate the choice of observable functions for Koopman analysis.
First, we note that to obtain a linear Koopman system that advances the
original states, it is helpful to include these states in the observable
subspace, as in DMD. We then categorize dynamical systems by whether or not
there exists a Koopman-invariant subspace that includes the state variables as
observables. In particular, we note that this is only possible when there is a
single isolated fixed point...

Link permanente para citações:

## Partial Dynamical Systems, Fell Bundles and Applications

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/11/2015
Português

Relevância na Pesquisa

67.091406%

This is a book about Partial Actions and Fell Bundles with applications to
C*-algebras generated by partial isometries. Here is the table of contents:
1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse
semigroups, 5-Topological partial dynamical systems, 6-Algebraic partial
dynamical systems, 7-Multipliers, 8-Crossed products, 9-Partial group
representations, 10-Partial group algebras, 11-C*-algebraic partial dynamical
systems, 12-Partial isometries, 13-Covariant representations of C*-algebraic
dynamical systems, 14-Partial representations subject to relations, 15-Hilbert
modules and Morita-Rieffel-equivalence, 16-Fell bundles, 17-Reduced
cross-sectional algebras, 18-Fell's absorption principle, 19-Graded
C*-algebras, 20-Amenability for Fell bundles, 21-Functoriality for Fell
bundles, 22-Functoriality for partial actions, 23-Ideals in graded algebras,
24-Pre-Fell-bundles, 25-Tensor products of Fell bundles, 26-Smash product,
27-Stable Fell bundles as partial crossed products, 28-Globalization in the
C*-context, 29-Topologically free partial actions, 30-Dilating partial
representations, 31-Semigroups of isometries, 32-Quasi-lattice ordered groups,
33-C*-algebras generated by semigroups of isometries, 34-Wiener-Hopf
C*-algebras...

Link permanente para citações:

## Eventual nonsensitivity and tame dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.16655%

#Mathematics - Dynamical Systems#Mathematics - Functional Analysis#Mathematics - General Topology#37Bxx, 46-xx, 54H15, 26A45

In this paper we characterize tame dynamical systems and functions in terms
of eventual non-sensitivity and eventual fragmentability. As a notable
application we obtain a neat characterization of tame subshifts $X \subset
\{0,1\}^{\mathbb Z}$: for every infinite subset $L \subseteq {\mathbb Z}$ there
exists an infinite subset $K \subseteq L$ such that $\pi_{K}(X)$ is a countable
subset of $\{0,1\}^K$. The notion of eventual fragmentability is one of the
properties we encounter which indicate some "smallness" of a family. We
investigate a "smallness hierarchy" for families of continuous functions on
compact dynamical systems, and link the existence of a "small" family which
separates points of a dynamical system $(G,X)$ to the representability of $X$
on "good" Banach spaces. For example, for metric dynamical systems the property
of admitting a separating family which is eventually fragmented is equivalent
to being tame. We give some sufficient conditions for coding functions to be
tame and, among other applications, show that certain multidimensional
analogues of Sturmian sequences are tame. We also show that linearly ordered
dynamical systems are tame and discuss examples where some universal dynamical
systems associated with certain Polish groups are tame.; Comment: 44 pages

Link permanente para citações:

## Sufficient Criteria for Existence of Pullback Attractors for Stochastic Lattice Dynamical Systems with Deterministic Non-autonomous Terms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/04/2014
Português

Relevância na Pesquisa

67.091406%

We consider the pullback attractors for non-autonomous dynamical systems
generated by stochastic lattice differential equations with non-autonomous
deterministic terms. We first establish a sufficient condition for existence of
pullback attractors of lattice dynamical systems with both non-autonomous
deterministic and random forcing terms. As an application of the abstract
theory, we prove the existence of a unique pullback attractor for the
first-order lattice dynamical systems with both deterministic non-autonomous
forcing terms and multiplicative white noise. Our results recover many existing
ones on the existences of pullback attractors for lattice dynamical systems
with autonomous terms or white noises.

Link permanente para citações:

## Consistency of maximum likelihood estimation for some dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.14241%

We consider the asymptotic consistency of maximum likelihood parameter
estimation for dynamical systems observed with noise. Under suitable conditions
on the dynamical systems and the observations, we show that maximum likelihood
parameter estimation is consistent. Our proof involves ideas from both
information theory and dynamical systems. Furthermore, we show how some
well-studied properties of dynamical systems imply the general statistical
properties related to maximum likelihood estimation. Finally, we exhibit
classical families of dynamical systems for which maximum likelihood estimation
is consistent. Examples include shifts of finite type with Gibbs measures and
Axiom A attractors with SRB measures.; Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org)

Link permanente para citações:

## Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/05/2015
Português

Relevância na Pesquisa

67.15048%

#Nonlinear Sciences - Chaotic Dynamics#Mathematical Physics#Mathematics - Dynamical Systems#Statistics - Applications

This special issue collects contributions from the participants of the
"Information in Dynamical Systems and Complex Systems" workshop, which cover a
wide range of important problems and new approaches that lie in the
intersection of information theory and dynamical systems. The contributions
include theoretical characterization and understanding of the different types
of information flow and causality in general stochastic processes, inference
and identification of coupling structure and parameters of system dynamics,
rigorous coarse-grain modeling of network dynamical systems, and exact
statistical testing of fundamental information-theoretic quantities such as the
mutual information. The collective efforts reported herein reflect a modern
perspective of the intimate connection between dynamical systems and
information flow, leading to the promise of better understanding and modeling
of natural complex systems and better/optimal design of engineering systems.

Link permanente para citações:

## On C*-algebras of irreversible algebraic dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.091406%

Extending the work of Cuntz and Vershik, we develop a general notion of
independence for commuting group endomorphisms. Based on this concept, we
initiate the study of irreversible algebraic dynamical systems, which can be
thought of as irreversible analogues of the dynamical systems considered by
Schmidt. To each irreversible algebraic dynamical system, we associate a
universal C*-algebra and show that it is a UCT Kirchberg algebra under natural
assumptions. Moreover, we discuss the structure of the core subalgebra, which
is closely related to generalised Bunce-Deddens algebras in the sense of
Orfanos. We also construct discrete product systems of Hilbert bimodules for
irreversible algebraic dynamical systems which allow us to view the associated
C*-algebras as Cuntz-Nica-Pimsner algebras. Besides, we prove a decomposition
theorem for semigroup crossed products of unital C*-algebras by semidirect
products of discrete, left cancellative monoids.; Comment: 41 pages

Link permanente para citações:

## Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/11/2014
Português

Relevância na Pesquisa

67.09927%

#Mathematics - Dynamical Systems#Mathematics - Analysis of PDEs#Mathematics - Classical Analysis and ODEs#34K08, 34K50, 35R60, 37H15, 37L55

This is the third part in a series of papers concerned with principal
Lyapunov exponents and principal Floquet subspaces of positive random dynamical
systems in ordered Banach spaces. The current part focuses on applications of
general theory, developed in the authors' paper "Principal Lyapunov exponents
and principal Floquet spaces of positive random dynamical systems. I. General
theory," Trans. Amer. Math. Soc. 365 (2013), pp. 5329-5365, to positive
continuous-time random dynamical systems on infinite dimensional ordered Banach
spaces arising from random parabolic equations and random delay systems. It is
shown under some quite general assumptions that measurable linear skew-product
semidynamical systems generated by random parabolic equations and by
cooperative systems of linear delay differential equations admit measurable
families of generalized principal Floquet subspaces, and generalized principal
Lyapunov exponents.; Comment: 42 pages; submitted for publication

Link permanente para citações:

## Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.08657%

#Mathematics - Dynamical Systems#Mathematics - Classical Analysis and ODEs#34C12, 37C65, 34D08, 37H15 (Primary) 15B52, 34F05 (Secondary)

This is the second part in a series of papers concerned with principal
Lyapunov exponents and principal Floquet subspaces of positive random dynamical
systems in ordered Banach spaces. The current part focuses on applications of
general theory, developed in the authors' paper "Principal Lyapunov exponents
and principal Floquet spaces of positive random dynamical systems. I. General
theory," Trans. Amer. Math. Soc., in press, to positive random dynamical
systems on finite-dimensional ordered Banach spaces. It is shown under some
quite general assumptions that measurable linear skew-product semidynamical
systems generated by measurable families of positive matrices and by strongly
cooperative or type-K strongly monotone systems of linear ordinary differential
equations admit measurable families of generalized principal Floquet subspaces,
generalized principal Lyapunov exponents, and generalized exponential
separations.; Comment: 31 pages; some clarifications have been made, and minor typos
corrected. Published in the Journal of Mathematical Analysis and Applications

Link permanente para citações:

## Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.1582%

#Mathematics - Dynamical Systems#Mathematics - Analysis of PDEs#Mathematics - Classical Analysis and ODEs#37H15, 37L55, 37A30 (Primary) 15B52, 34F05, 35R60 (Secondary)

This is the first of a series of papers concerned with principal Lyapunov
exponents and principal Floquet subspaces of positive random dynamical systems
in ordered Banach spaces. It focuses on the development of general theory.
First, the notions of generalized principal Floquet subspaces, generalized
principal Lyapunov exponents, and generalized exponential separations for
general positive random dynamical systems in ordered Banach spaces are
introduced, which extend the classical notions of principal Floquet subspaces,
principal Lyapunov exponents, and exponential separations for strongly positive
deterministic systems in strongly ordered Banach to general positive random
dynamical systems in ordered Banach spaces. Under some quite general
assumptions, it is then shown that a positive random dynamical system in an
ordered Banach space admits a family of generalized principal Floquet
subspaces, a generalized principal Lyapunov exponent, and a generalized
exponential separation. We will consider in the forthcoming parts applications
of the general theory developed in this part to positive random dynamical
systems arising from a variety of random mappings and differential equations,
including random Leslie matrix models, random cooperative systems of ordinary
differential equations...

Link permanente para citações:

## Kosambi-Cartan-Chern (KCC) theory for higher order dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.25202%

The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical
method for the investigation of the properties of dynamical systems. The KCC
theory introduces a geometric description of the time evolution of a dynamical
system, with the solution curves of the dynamical system described by methods
inspired by the theory of geodesics in a Finsler spaces. The evolution of a
dynamical system is geometrized by introducing a non-linear connection, which
allows the construction of the KCC covariant derivative, and of the deviation
curvature tensor. In the KCC theory the properties of any dynamical system are
described in terms of five geometrical invariants, with the second one giving
the Jacobi stability of the system. Usually, the KCC theory is formulated by
reducing the dynamical evolution equations to a set of second order
differential equations. In the present paper we introduce and develop the KCC
approach for dynamical systems described by systems of arbitrary
$n$-dimensional first order differential equations. We investigate in detail
the properties of the $n$-dimensional autonomous dynamical systems, as well as
the relationship between the linear stability and the Jacobi stability. As a
main result we find that only even-dimensional dynamical systems can exhibit
both Jacobi stability and instability behaviors...

Link permanente para citações:

## The steady states of coupled dynamical systems compose according to matrix arithmetic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/12/2015
Português

Relevância na Pesquisa

67.24096%

Open dynamical systems are mathematical models of machines that take input,
change their internal state, and produce output. For example, one may model
anything from neurons to robots in this way. Several open dynamical systems can
be arranged in series, in parallel, and with feedback to form a new dynamical
system---this is called compositionality---and the process can be repeated in a
fractal-like manner to form more complex systems of systems. One issue is that
as larger systems are created, their state space grows exponentially.
In this paper a technique for calculating the steady states of a system of
systems, in terms of the steady states of its component dynamical systems, is
provided. These are organized into "steady state matrices" which are strongly
analogous to bifurcation diagrams. It is shown that the compositionality
structure of dynamical systems fits with the familiar monoidal structure for
the steady state matrices, where serial, parallel, and feedback composition of
matrices correspond to multiplication, Kronecker product, and partial trace
operations. The steady state matrices of dynamical systems respect this
compositionality structure, exponentially reducing the complexity involved in
studying the steady states of composite dynamical systems.; Comment: 40 pages

Link permanente para citações:

## Cycle Equivalence of Graph Dynamical Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/02/2008
Português

Relevância na Pesquisa

67.095566%

Graph dynamical systems (GDSs) can be used to describe a wide range of
distributed, nonlinear phenomena. In this paper we characterize cycle
equivalence of a class of finite GDSs called sequential dynamical systems SDSs.
In general, two finite GDSs are cycle equivalent if their periodic orbits are
isomorphic as directed graphs. Sequential dynamical systems may be thought of
as generalized cellular automata, and use an update order to construct the
dynamical system map.
The main result of this paper is a characterization of cycle equivalence in
terms of shifts and reflections of the SDS update order. We construct two
graphs C(Y) and D(Y) whose components describe update orders that give rise to
cycle equivalent SDSs. The number of components in C(Y) and D(Y) is an upper
bound for the number of cycle equivalence classes one can obtain, and we
enumerate these quantities through a recursion relation for several graph
classes. The components of these graphs encode dynamical neutrality, the
component sizes represent periodic orbit structural stability, and the number
of components can be viewed as a system complexity measure.

Link permanente para citações:

## Second order forward-backward dynamical systems for monotone inclusion problems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/03/2015
Português

Relevância na Pesquisa

67.091406%

#Mathematics - Optimization and Control#Mathematics - Dynamical Systems#Mathematics - Functional Analysis#34G25, 47J25, 47H05, 90C25

We begin by considering second order dynamical systems of the from $\ddot
x(t) + \Gamma (\dot x(t)) + \lambda(t)B(x(t))=0$, where $\Gamma: {\cal
H}\rightarrow{\cal H}$ is an elliptic bounded self-adjoint linear operator
defined on a real Hilbert space ${\cal H}$, $B: {\cal H}\rightarrow{\cal H}$ is
a cocoercive operator and $\lambda:[0,+\infty)\rightarrow [0,+\infty)$ is a
relaxation function depending on time. We show the existence and uniqueness of
strong global solutions in the framework of the Cauchy-Lipschitz-Picard Theorem
and prove weak convergence for the generated trajectories to a zero of the
operator $B$, by using Lyapunov analysis combined with the celebrated Opial
Lemma in its continuous version. The framework allows to address from similar
perspectives second order dynamical systems associated with the problem of
finding zeros of the sum of a maximally monotone operator and a cocoercive one.
This captures as particular case the minimization of the sum of a nonsmooth
convex function with a smooth convex one and allows us to recover and improve
several results from the literature concerning the minimization of a convex
smooth function subject to a convex closed set by means of second order
dynamical systems. When considering the unconstrained minimization of a smooth
convex function we prove a rate of ${\cal O}(1/t)$ for the convergence of the
function value along the ergodic trajectory to its minimum value. A similar
analysis is carried out also for second order dynamical systems having as first
order term $\gamma(t) \dot x(t)$...

Link permanente para citações:

## Continuation of solutions of coupled dynamical systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/08/2007
Português

Relevância na Pesquisa

67.111577%

Recently, the synchronization of coupled dynamical systems has been widely
studied. Synchronization is referred to as a process wherein two (or many)
dynamical systems are adjusted to a common behavior as time goes to infinity,
due to coupling or forcing. Therefore, before discussing synchronization, a
basic problem on continuation of the solution must be solved: For given initial
conditions, can the solution of coupled dynamical systems be extended to the
infinite interval $[0,+\infty)$? In this paper, we propose a general model of
coupled dynamical systems, which includes previously studied systems as special
cases, and prove that under the assumption of QUAD, the solution of the general
model exists on $[0,+\infty)$.

Link permanente para citações:

## Hyperbolic Dynamical Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/04/2008
Português

Relevância na Pesquisa

67.127363%

The theory of uniformly hyperbolic dynamical systems was initiated in the
1960's (though its roots stretch far back into the 19th century) by S. Smale,
his students and collaborators, in the west, and D. Anosov, Ya. Sinai, V.
Arnold, in the former Soviet Union. It came to encompass a detailed description
of a large class of systems, often with very complex evolution. Moreover, it
provided a very precise characterization of structurally stable dynamics, which
was one of its original main goals. The early developments were motivated by
the problem of characterizing structural stability of dynamical systems, a
notion that had been introduced in the 1930's by A. Andronov and L. Pontryagin.
Inspired by the pioneering work of M. Peixoto on circle maps and surface flows,
Smale introduced a class of gradient-like systems, having a finite number of
periodic orbits, which should be structurally stable and, moreover, should
constitute the majority (an open and dense subset) of all dynamical systems.
Stability and openness were eventually established, in the thesis of J. Palis.
However, contemporary results of M. Levinson, based on previous work by M.
Cartwright and J. Littlewood, provided examples of open subsets of dynamical
systems all of which have an infinite number of periodic orbits.; Comment: 22 pages...

Link permanente para citações: