Uniform hyperbolicity along periodic orbits-Reference-Cited by-同舟云学术

Uniform hyperbolicity along periodic orbits

Published:2013-05-03 Issue:9 Volume:141 Page:3107-3118
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Fakhari Abbas

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 C^1 -generic homoclinic class implies hyperbolicity. It is shown that for a C 1 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 C^1 -dichotomy theorems.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2013-141-09/S0002-9939-2013-11553-4/S0002-9939-2013-11553-4.pdf

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