Volume Preserving Diffeomorphisms with Inverse Shadowing
Abstract
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.
Cite
@article{arxiv.1105.5917,
title = {Volume Preserving Diffeomorphisms with Inverse Shadowing},
author = {Manseob Lee},
journal= {arXiv preprint arXiv:1105.5917},
year = {2012}
}
Comments
10 pages. arXiv admin note: text overlap with arXiv:1104.5063