Super exponential divergence of periodic points for C1-generic partially hyperbolic homoclinic classes
Abstract
A diffeomorphism f is called super exponential divergent if for every r>1, the lower limit of #Pern(f)/rn diverges to infinity as n tends to infinity, where Pern(f) is the set of all periodic points of f with period n. This property is stronger than the usual super exponential growth of the number of periodic points. We show that for a three dimensional manifold M, there exists an open subset O of Diff1(M) such that diffeomorphisms with super exponential divergent property form a dense subset of O in the C1-topology. A relevant result of non super exponential divergence for diffeomorphisms in a locally generic subset of Diffr(M) (r=1,2,...∞) is also shown.
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