On Invariant Subsets of Hyberbolic Sets

Morris W. Hirsch

A chapter in Essays on Topology and Related Topics, 1970, pp 126-135 from Springer

Abstract: Abstract Let f: M→M be a diffeomorphism and suppose Λ ⊂ M is a hyperbolic subset of f. What kind of compact invariant sets can lie in Λ? Even for Anosov diffeomorphisms—where Λ = M—little is known about this question. In this note we exploit the theory of stable manifolds to find necessary conditions on invariant subsets of certain kinds of hyperbolic sets.

Keywords: Periodic Point; Unstable Manifold; Stable Manifold; Invariant Subset; Invariant Submanifold (search for similar items in EconPapers)
Date: 1970
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-49197-9_12

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DOI: 10.1007/978-3-642-49197-9_12

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