ERGODIC CLOSING AND NEW CRITERIA FOR HYPERBOLICITY BASED ON PERIODIC SETS
Augusto Armando Castro Jr.
Nonuniform Hyperbolicity | shadowing | periodic Sets
We prove some criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild hyperbolicity condition holds for the periodic points of any diﬀeomorphism in a residual subset of a C 1 -open set U then there exists an open and dense subset A ⊂ U of Axiom A diﬀeomorphisms. Moreover, we also prove a noninvertible version of Ergodic Closing Lemma which we use to prove a counterpart of this result for local diﬀeomorphisms.