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 .
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© 1987 Springer-Verlag Berlin Heidelberg
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Shub, M. (1987). Filtrations. In: Global Stability of Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1947-5_2
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DOI: https://doi.org/10.1007/978-1-4757-1947-5_2
Publisher Name: Springer, New York, NY
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