Horseshoes for diffeormorphisms preserving hyperbolic measures
  We give extensions of Katok's horseshoe constructions, comment on related results, and provide a self-contained proof. We consider either a $C^{1+\alpha}$ diffeomorphism preserving a hyperbolic measure or a $C^1$ diffeomorphism preserving a hyperbolic measure whose support admits a dominated splitting. 
Katrin Gelfert
math.DS