Displaying similar documents to “On foundations of the Conley index theory”

The Conley index theory: A brief introduction

Konstantin Mischaikow (1999)

Banach Center Publications

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A brief introduction to the Conley index theory is presented. The emphasis is the fundamental ideas of Conley's approach to dynamical systems and how it avoids some of the difficulties inherent in the study of nonlinear systems.

Reconstructing the global dynamics of attractors via the Conley index

Christopher McCord (1999)

Banach Center Publications

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Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy...

Index filtrations and Morse decompositions for discrete dynamical systems

P. Bartłomiejczyk, Z. Dzedzej (1999)

Annales Polonici Mathematici

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On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.

Foreword, Contents

Konstantin Mischaikow, Marian Mrozek, Piotr Zgliczyński (1999)

Banach Center Publications

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Dynamical systems and shapes.

J.J. Sánchez-Gabites (2008)

RACSAM

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This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.