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

Tomasz Kaczynski (1999)

Banach Center Publications

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.

Connection matrices and transition matrices

Christopher McCord, James Reineck (1999)

Banach Center Publications

This paper is an introduction to connection and transition matrices in the Conley index theory for flows. Basic definitions and simple examples are discussed.

Rosen fractions and Veech groups, an overly brief introduction

Thomas A. Schmidt (2009)

Actes des rencontres du CIRM

We give a very brief, but gentle, sketch of an introduction both to the Rosen continued fractions and to a geometric setting to which they are related, given in terms of Veech groups. We have kept the informal approach of the talk at the Numerations conference, aimed at an audience assumed to have heard of neither of the topics of the title.The Rosen continued fractions are a family of continued fraction algorithms, each gives expansions of real numbers in terms of elements of a corresponding algebraic...

The Conley index theory: A brief introduction

Konstantin Mischaikow (1999)

Banach Center Publications

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.

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