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The Conley index for maps in absence of compactness

Published online by Cambridge University Press:  14 November 2011

Marco Degiovanni  and
Marian Mrozek
Marco Degiovanni
Affiliation:
Università Cattolica del Sacro Cuore, Dipartimento di Matematica, Via Trieste 17, I-25121 Brescia, Italy
Marian Mrozek
Affiliation:
Uniwersytet Jagielloński, Katedra Informatyki, ul. Kopernika 27, PL-31-501 Kraków, Poland
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Synopsis

We construct the Conley index for maps. We do not assume any compactness of map or space. We prove the Ważewski property, additivity property and continuation property.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 1 , 1993 , pp. 75 - 94
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Benci, V.. A new approach to the Morse-Conley theory and some applications. Ann. Mat. Pura Appl. (4) 158 (1991), 231–305.CrossRefGoogle Scholar
2Benci, V. and Degiovanni, M.. Morse–Conley Theory (in preparation).Google Scholar
3Conley, C. C.. Isolated Invariant Sets and the Morse Index, CBMS Regional Conference Series in Mathematics 38 (Providence, R.I.: American Mathematical Society, 1978).CrossRefGoogle Scholar
4Mrozek, M.. Leray functor and the cohomological Conley index for discrete dynamical systems. Trans. Amer. Math. Soc. 318 (1990), 149–178.CrossRefGoogle Scholar
5Mrozek, M. and Rybakowski, K. P.. A cohomological Conley index for maps on metric spaces. J. Differential Equations 90 (1991), 143–171.CrossRefGoogle Scholar
6Robbin, J. W. and Salamon, D.. Dynamical systems, shape theory and the Conley index. Ergodic Theory Dynamical Systems 8 (1988), 375–393.Google Scholar
7Rybakowski, K. P.. The Homotopy Index and Partial Differential Equations (Berlin: Springer, 1987).CrossRefGoogle Scholar
8Ważewski, T.. Sur un principe topologique pour l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires. Ann. Soc. Polon. Math. 20 (1947), 279–313.Google Scholar