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4 Banach Center Publications

4 1999

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The Conley index theory: A brief introduction

100%

Mischaikow K.

tom 47

nr 1

9-19

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.

Cubical approximation and computation of homology

51%

Kalies W. D. , Mischaikow K. , Watson G.

tom 47

nr 1

115-131

The purpose of this article is to introduce a method for computing the homology groups of cellular complexes composed of cubes. We will pay attention to issues of storage and efficiency in performing computations on large complexes which will be required in applications to the computation of the Conley index. The algorithm used in the homology computations is based on a local reduction procedure, and we give a subquadratic estimate of its computational complexity. This estimate is rigorous in two dimensions, and we conjecture its validity in higher dimensions.

Directional transition matrix

51%

Kokubu H. , Mischaikow K. , Oka H.

tom 47

nr 1

133-144

We present a generalization of topological transition matrices introduced in [6].

Foreword, Contents

32%

Mischaikow K. , Mrozek M. , Zgliczyński P.

tom 47

nr 1

1-7