Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing

Abstract

Let f be a volume-preserving diffeomorphism of a closed C1 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 diffeomorphisms which satisfy the weak shadowing property, (b) f belongs to the C1-interior of the set of volume-preserving diffeomorphisms which satisfy the limit weak shadowing property, (c) f is Anosov.

9 pages. arXiv admin note: substantial text overlap with arXiv:1105.5917

Cited by in corpus (2)

• Stably weakly shadowing symplectomorphisms are partially hyperbolic
• Stable weakly shadowable volume-preserving systems are volume-hyperbolic