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Transactions of the American Mathematical Society

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Topological entropy of homoclinic closures

Author: Leonardo Mendoza
Journal: Trans. Amer. Math. Soc. 311 (1989), 255-266
MSC: Primary 58F11; Secondary 28D20, 58F15
MathSciNet review: 974777
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Abstract: In this paper we study the topological entropy of certain invariant sets of diffeomorphisms, namely the closure of the set of transverse homoclinic points associated with a hyperbolic periodic point, in terms of the growth rate of homoclinic orbits. First we study homoclinic closures which are hyperbolic in $ n$-dimensional compact manifolds. Using the pseudo-orbit shadowing property of basic sets we prove a formula similar to Bowen's one on the growth of periodic points. For the nonuniformly hyperbolic case we restrict our attention to compact surfaces.

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Article copyright: © Copyright 1989 American Mathematical Society

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