Uniform hyperbolicity along periodic orbits

Fakhari, Abbas

doi:10.1090/S0002-9939-2013-11553-4

Uniform hyperbolicity along periodic orbits
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by Abbas Fakhari PDF

Proc. Amer. Math. Soc. 141 (2013), 3107-3118 Request permission

Abstract:

We introduce the notion of uniform hyperbolicity along periodic orbits (UHPO) for homoclinic classes and provide equivalent conditions under which the UHPO property on a $C^1$-generic homoclinic class implies hyperbolicity. It is shown that for a $C^1$-generic locally maximal homoclinic class the UHPO property is equivalent to the non-existence of zero Lyapunov exponents. Using the notion of UHPO, we also give new proofs for some recent $C^1$-dichotomy theorems.

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