Uniform hyperbolicity along periodic orbits (Q2845460)

The paper under review is a very interesting work where the author introduces the notion of uniform hyperbolicity along periodic orbits (UHPO) for homoclinic classes.NEWLINENEWLINE The paper provides equivalent conditions under which the UHPO property on a \(C^1\)-generic homoclinic class implies hyperbolicity. Moreover, it is shown that for a \(C^1\)-generic locally maximal homoclinic class, the UHPO property is equivalent to the nonexistence of zero Lyapunov exponents. Using the notion of UHPO, a new proof is given for some recent \(C^1\)-dichotomy theorems.