The distribution of the periodic orbits with open deviation in C 1+α non-uniformly hyperbolic systems

Abstract

Let f: M → M be a C 1+α diffeomorphism on a smooth compact Riemannian manifold M and Λ be a Pesin set associated with the ergodic hyperbolic measure µ. Then f: Λ → Λ forms a non-uniformly hyperbolic system. We concern with the distribution of the periodic orbits whose time averages are apart from the space average of µ. Finally, we derive a large deviation result for these periodic orbits with open deviation property.