Author Index
(2016)
Archivum Mathematicum
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(2016)
Archivum Mathematicum
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T. Frey (1966)
Applicationes Mathematicae
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Mitrea, Marius (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Wenguang Zhai (2006)
Acta Arithmetica
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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.
Konstantin Mischaikow, Marian Mrozek, Piotr Zgliczyński (1999)
Banach Center Publications
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Obukhovskii, Valeri, Zecca, Pietro, Zvyagin, Victor (2002)
Abstract and Applied Analysis
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Roman Srzednicki (1999)
Banach Center Publications
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The Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the...
Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz (2016)
Czechoslovak Mathematical Journal
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We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.
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.