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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 C1-generic homoclinic class implies hyperbolicity. It is shown that for a C1-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 C1-dichotomy theorems.

Uniform hyperbolicity along periodic orbits