English

Volume Preserving Diffeomorphisms with Inverse Shadowing

Dynamical Systems 2012-03-19 v3

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.

Keywords

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

R2 v1 2026-06-21T18:14:29.200Z