Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing

Details Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing

2011-04-27

arxiv.org/abs/1104.5063v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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