We show that if a differentiable map of a smooth manifold has a non-atomic ergodic hyperbolic measure then the topological entropy is positive and the space contains a hyperbolic horseshoe. Moreover we give some relations between hyperbolic measures and periodic points for differentiable maps. These are generalized contents of the results obtained by Katok for diffeomorphisms.
"Shadowing Property of Non-Invertible Maps with Hyperbolic Measures." Tokyo J. Math. 22 (1) 145 - 166, June 1999. https://doi.org/10.3836/tjm/1270041619