The Specification Property for Flows from the Robust and Generic Viewpoint

Alexander Arbieto; Laura Senos; Tatiana Sodero

The Specification Property for Flows from the Robust and Generic Viewpoint

Dynamical Systems 2011-07-07 v2

Authors: Alexander Arbieto , Laura Senos , Tatiana Sodero

Abstract

We prove that if $X|_\Lambda$ has the weak specification property robustly, where $\Lambda$ is an isolated set, then $\Lambda$ is a hyperbolic topologically mixing set and, as a consequence, if $X$ is a vector field that has the weak specification property robustly on a closed manifold $M$ , then the flow $X_t$ is a topologically mixing Anosov flow. Also we prove that there exists a residual subset $\SR \in \Mundo$ so that if $X \in \SR$ and $X$ has the weak specification property, then $X_t$ is an Anosov flow.

Keywords

anosov flows geodesic flow

Cite

@article{arxiv.1101.3445,
  title  = {The Specification Property for Flows from the Robust and Generic Viewpoint},
  author = {Alexander Arbieto and Laura Senos and Tatiana Sodero},
  journal= {arXiv preprint arXiv:1101.3445},
  year   = {2011}
}

Comments

We improve our previous results and correct some typos

The Specification Property for Flows from the Robust and Generic Viewpoint

Abstract

Keywords

Cite

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