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

Let f ： M → M be a C^1＋α diffeomorphism on a smooth compact Riemannian manifold M and A be a Pesin set associated with the ergodic hyperbolic measure μ. Then f ： A → A 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.

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.