A topological persistence theorem for normally hyperbolic manifolds via the Conley index
HTML articles powered by AMS MathViewer
- by Andreas Floer PDF
- Trans. Amer. Math. Soc. 321 (1990), 647-657 Request permission
Abstract:
We prove that the cohomology ring of a normally hyperbolic manifold of a diffeomorphism $f$ persists under perturbation of $f$. We do not make any quantitative assumptions on the expansion and contraction rates of $Df$ on the normal and the tangent bundles of $N$.References
- Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, vol. 38, American Mathematical Society, Providence, R.I., 1978. MR 511133
- Neil Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971/72), 193–226. MR 287106, DOI 10.1512/iumj.1971.21.21017
- Andreas Floer, A refinement of the Conley index and an application to the stability of hyperbolic invariant sets, Ergodic Theory Dynam. Systems 7 (1987), no. 1, 93–103. MR 886372, DOI 10.1017/S0143385700003825
- Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
- Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
- M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977. MR 0501173
- Jiří Jarník and Jaroslav Kurzweil, On invariant sets and invariant manifolds of differential systems, J. Differential Equations 6 (1969), 247–263. MR 249729, DOI 10.1016/0022-0396(69)90016-3 J. McCarthy, Stability of invariant manifolds, Bull. Amer. Math. Soc. 61 (1955), 149-150.
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 321 (1990), 647-657
- MSC: Primary 58F15; Secondary 58F30
- DOI: https://doi.org/10.1090/S0002-9947-1990-0968418-4
- MathSciNet review: 968418