Volume Preserving Diffeomorphisms with Inverse Shadowing

Details Volume Preserving Diffeomorphisms with Inverse Shadowing Volume Preserving Diffeomorphisms with Inverse Shadowing

2011-05-30

arxiv.org/abs/1105.5917v3

Mathematics

Dynamical Systems

10 pages. arXiv admin note: text overlap with arXiv:1104.5063

Scientific paper

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.

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