Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A topological persistence theorem for normally hyperbolic manifolds via the Conley index


Author: Andreas Floer
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. D. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math., no. 38, Amer. Math. Soc., Providence, R. I., 1978. MR 511133 (80c:58009)
  • [2] N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971), 193-226. MR 0287106 (44:4313)
  • [3] A. Floer, A refinement of the Conley index and an application to the stability of hyperbolic invariant sets, Ergodic Theory and Dynamical Systems 7 (1987), 93-103. MR 886372 (88g:58143)
  • [4] J. K. Hale, Ordinary differential equations, Wiley, New York, 1969. MR 0419901 (54:7918)
  • [5] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978. MR 514561 (80k:53081)
  • [6] M. W. Hirsch, C. C. Pugh and M. Shub, Invariant manifolds, Lectures Notes in Math., vol. 583, Springer-Verlag, 1977. MR 0501173 (58:18595)
  • [7] J. Jarik and J. Kurzweil, On invariant sets and invariant manifolds of differential systems, J. Differential Equations 6 (1969), 247-263. MR 0249729 (40:2970)
  • [8] J. McCarthy, Stability of invariant manifolds, Bull. Amer. Math. Soc. 61 (1955), 149-150.
  • [9] E. Spanier, Algebraic topology, McGwraw-Hill, New York, 1966. MR 0210112 (35:1007)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F15, 58F30

Retrieve articles in all journals with MSC: 58F15, 58F30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0968418-4
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society