Abstract
We consider a few applications of Mañé’s C 2 C^2 Connecting Lemma. These are the C 2 C^2 creation of homoclinic points associated to a basic set (i.e., isolated transitive hyperbolic set), a C 2 C^2 locally generic criterion to know whether a given point belongs to the stable set of hyperbolic homoclinic classes, and that measurably hyperbolic diffeomorphisms (i.e., having the closure of supports of all invariant measures as a countable union of disjoint basic sets) are C 2 C^2 generically uniformly hyperbolic diffeomorphisms.
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