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A refinement of the Conley index and an application to the stability of hyperbolic invariant sets

  • Andreas Floer (a1)
Abstract

A compact and isolated invariant set of a continuous flow possesses a so called Conley index, which is the homotopy type of a pointed compact space. For this index a well known continuation property holds true. Our aim is to prove in this context a continuation theorem for the invariant set itself, using an additional structure. This refinement of Conley's index theory will then be used to prove a global and topological continuation-theorem for normally hyperbolic invariant sets.

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COPYRIGHT: © Cambridge University Press 1987
References
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[1]Benci, V.. MRC-report, to appear.
[2]Conley, C. C.. Isolated Invariant Sets and the Morse Index. CBMS, Regional Conf. Series in Math., vol. 38 (1978).
[3]Conley, C. & Zehnder, E.. Morse type index theory for Hamiltonian equations. Comm. Pure and Appl. Math. XXXVII (1984), 207–253.
[4]Fadell, F. T. & Rabinowitz, P. H.. Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Inv. Math. 45 (1978), 139–174.
[5]Fenichel, N.. Persistence and smoothness of invariant manifolds for flows. Ind. Univ. Math. J. 21, No. 3 (1971).
[6]Floer, A.. Proof of the Arnold conjecture for surfaces and generalizations for certain Kähler manifolds. To appear in Duke Math. J., vol. 42.
[7]Floer, A. & Zehnder, E.. Fixed points results for symplectic maps related to the Arnold-Conjecture. Proceedings of workshop in Dynamical Systems & Bifurcations, Groningen 16–19. 04 1984.
[8]Helgason, S.. Differential Geometry, Lie groups and Symmetric Spaces. New York, 1978: Academic Press.
[9]Hirsch, M. W., Pugh, C. C. & Shub, M.. Invariant Manifolds. Lecture Notes in Math. 583, Berlin-Heidelberg-New York 1977: Springer.
[10]Spanier, E.. Algebraic Topology. New York 1966: McGraw Hill.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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