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Locally maximal homoclinic classes for generic diffeomorphisms. (English) Zbl 1379.37044

Summary: Let \(M\) be a closed smooth \(d(\geq 2)\) dimensional Riemannian manifold and let \(f : M \to M\) be a diffeomorphism. For \(C^1\) generic \(f\), a locally maximal homogeneous homoclinic class is hyperbolic.

MSC:

37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C20 Generic properties, structural stability of dynamical systems
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
53B21 Methods of local Riemannian geometry
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