Displaying similar documents to “Directional transition matrix”

Connection matrices and transition matrices

Christopher McCord, James Reineck (1999)

Banach Center Publications

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

Connection matrix pairs

David Richeson (1999)

Banach Center Publications

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We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and...

Connection matrix theory for discrete dynamical systems

Piotr Bartłomiejczyk, Zdzisław Dzedzej (1999)

Banach Center Publications

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In [C] and [F1] the connection matrix theory for Morse decomposition is developed in the case of continuous dynamical systems. Our purpose is to study the case of discrete time dynamical systems. The connection matrices are matrices between the homology indices of the sets in the Morse decomposition. They provide information about the structure of the Morse decomposition; in particular, they give an algebraic condition for the existence of connecting orbit set between different Morse...

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.

Foreword, Contents

Konstantin Mischaikow, Marian Mrozek, Piotr Zgliczyński (1999)

Banach Center Publications

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