Volume Preserving Diffeomorphisms with Inverse Shadowing

Manseob Lee

Published 2011-05-30, updated 2012-03-05Version 3

Let f be a volume-preserving diffeomorphism of a closed C^\infty n-dimensional Riemannian manifold M: In this paper, we prove the equivalence between the following conditions: (a) f belongs to the C1-interior of the set of volume-preserving diffeoeomorphisms which satisfy the inverse shadowing property with respect to the continuous methods. (b) f belongs to the C1-interior of the set of volume-preserving diffeomorphisms which satisfy the weak inverse shadowing property with respect to the continuous methods. (c) f belongs to the C1-interior of the set of volume-preserving diffeomorphisms which satisfy the orbital inverse shadowing property with respect to the continuous methods, (d) f is Anosov.