Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes (1507.08253v1)

Published 29 Jul 2015 in math.DS

Abstract: We prove that, for $C^1$-generic diffeomorphisms, if a homoclinic class is not hyperbolic, then there is a non-hyperbolic ergodic measure supported on it. This proves a conjecture by D\'iaz and Gorodetski [28]. We also discuss the conjectured existence of periodic points with different stable dimension in the class.

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