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 .
KeywordsLimit Point Disjoint Union Global Stability Compact Neighborhood Nest Sequence
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