Author Index
(2015)
Archivum Mathematicum
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(2015)
Archivum Mathematicum
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(2016)
Archivum Mathematicum
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T. Frey (1966)
Applicationes Mathematicae
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Wenguang Zhai (2006)
Acta Arithmetica
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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...
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.
Obukhovskii, Valeri, Zecca, Pietro, Zvyagin, Victor (2002)
Abstract and Applied Analysis
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Konstantin Mischaikow, Marian Mrozek, Piotr Zgliczyński (1999)
Banach Center Publications
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Razvan, M.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Miguel Ramos, Luís Sanchez (1995)
Manuscripta mathematica
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Marek Izydorek, Krzysztof P. Rybakowski (2002)
Fundamenta Mathematicae
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Consider the ordinary differential equation (1) ẋ = Lx + K(x) on an infinite-dimensional Hilbert space E, where L is a bounded linear operator on E which is assumed to be strongly indefinite and K: E → E is a completely continuous but not necessarily locally Lipschitzian map. Given any isolating neighborhood N relative to equation (1) we define a Conley-type index of N. This index is based on Galerkin approximation of equation (1) by finite-dimensional...