Displaying similar documents to “Reconstructing the global dynamics of attractors via the Conley index”

On foundations of the Conley index theory

Roman Srzednicki (1999)

Banach Center Publications

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The Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the...

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.

Some remarks on tubular neighborhoods and gluing in Morse-Floer homology

Maurizio Rinaldi, Krzysztof Rybakowski (1999)

Banach Center Publications

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We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.

Foreword, Contents

Konstantin Mischaikow, Marian Mrozek, Piotr Zgliczyński (1999)

Banach Center Publications

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Conley index for set-valued maps: from theory to computation

Tomasz Kaczynski (1999)

Banach Center Publications

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Recent results on the Conley index theory for discrete multi-valued dynamical systems with their consequences for the computation of the index for representable maps are recapitulated. The terminology is simplified with respect to previous presentations, some superfluous hypotheses are abandoned and some conclusions are proved in a simpler way.

Stability and gradient dynamical systems.

Jack K. Hale (2004)

Revista Matemática Complutense

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The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which...