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Filtrations

In: Global Stability of Dynamical Systems

Author

Listed:
  • Michael Shub

    (IBM, Thomas J. Watson Research Center)

Abstract

One way to understand the recurrence of a homeomorphism is to try to build up the underlying manifold from simpler pieces, each of which isolates and asymptotically specifies an invariant set. With this in mind we make several definitions. Given a homeomorphism f, of M, a filtration M adapted to f is a nested sequence Ø = M 0 ⊂ M 1 ⊂ ··· ⊂ M k = M of smooth, compact codimension 0 submanifolds with boundary of M, such that f(M i ), ⊂ Int M i .

Suggested Citation

  • Michael Shub, 1987. "Filtrations," Springer Books, in: Global Stability of Dynamical Systems, chapter 0, pages 8-12, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-1947-5_2
    DOI: 10.1007/978-1-4757-1947-5_2
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