Approximation of Oseledets Splittings
  We prove that the Oseledets splittings of an ergodic hyperbolic measure of a $C^{1+ r}$ diffeomorphism can be approximated by that of atomic measures on hyperbolic periodic orbits. This removes the assumption on simple spectrum in \cite{Liang} and strengthens Katok's closing lemma. 
Chao Liang, Gang Liao and Wenxiang Sun
math.DS