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.
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Bibliography
Franks, J.: Anosov diffeomorphisms. Proceedings of the A.M.S. Summer Institute on Global Analysis 1968.
Hirsch, M. W., and C. C. Pugh: Stable manifolds and hyperbolic sets. Proceedings of the A. M. S. Summer Institute on Global Analysis 1968.
Hirsch, M. W., and C. C. Pugh: Stable manifolds and hyperbolic sets. Bull. Amer. Math. Soc. 75, 149 — 152 (1969).
Hirsch, M. W., J. Palis, C. Pugh and M. Shub: Neighborhoods of hyperbolic sets. To appear.
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© 1970 Springer-Verlag Berlin · Heidelberg
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Hirsch, M.W. (1970). On Invariant Subsets of Hyberbolic Sets. In: Essays on Topology and Related Topics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49197-9_12
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DOI: https://doi.org/10.1007/978-3-642-49197-9_12
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