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Connection matrix theory for discrete dynamical systems

100%

Bartłomiejczyk P., Dzedzej Z.

Banach Center Publications

1999

tom 47

nr 1

67-78

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 sets.

Index filtrations and Morse decompositions for discrete dynamical systems

100%

Bartłomiejczyk P., Dzedzej Z.

Annales Polonici Mathematici

1999

tom 72

nr 1

51-70

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.

Connection matrix pairs

88%

Richeson D.

Banach Center Publications

1999

tom 47

nr 1

219-232

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 [R2].

Ograniczanie wyników

2 Banach Center Publications

1 Annales Polonici Mathematici

2 Bartłomiejczyk P.

2 Dzedzej Z.

1 Richeson D.

3 1999

Wyniki wyszukiwania

Connection matrix theory for discrete dynamical systems

Index filtrations and Morse decompositions for discrete dynamical systems

Connection matrix pairs