# On the Average Shadowing Property and Hyperbolicity

### New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 189-194

Department of Mathematics,

Iran

Abstract In this paper we show that there is a residual set $R\subset Diff^1(M^3)$ such that if $f\in R$ is tame and has the average shadowing property, then f is Anosov or there is a non-hyperbolic ergodic measure with support on the whole of the manifold M.

Keywords Average shadowing property, δ-average-pseudo-orbit, Dominated splitting, non hyperbolic ergodic measure.

Classification (MSC2000) 54H20: 37C05, 37C20, 37D25, 37D30.