Index pairs and the fixed point index for semidynamical systems with discrete time
Marian Mrozek (1989)
Fundamenta Mathematicae
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Marian Mrozek (1989)
Fundamenta Mathematicae
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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.
J.J. Sánchez-Gabites (2008)
RACSAM
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This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.
Marian Gidea (1999)
Banach Center Publications
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We define a new cohomological index of Conley type associated to any bi-infinite sequence of neighborhoods that satisfies a certain isolation condition. We use this index to study the chaotic dynamics on invariant sets which decompose as countable unions of pairwise disjoint (mod 0) compact pieces.
Razvan, M.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Marian Mrozek (1995)
Banach Center Publications
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Artur Pruszko (1999)
Banach Center Publications
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Topological spaces with generalized symmetries are defined and extensions of the Conley index of a compact isolated invariant set of the flow preserving the structures introduced are proposed. One of the two new indexes is constructed with no additional assumption on the examined set in terms of symmetry invariance.
Andrzej Granas (1972)
Bulletin de la Société Mathématique de France
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