The Specification Property for Flows from the Robust and Generic Viewpoint

Details The Specification Property for Flows from the Robust and Generic Viewpoint The Specification Property for Flows from the Robust and Generic Viewpoint

2011-01-18

arxiv.org/abs/1101.3445v2

Mathematics

Dynamical Systems

We improve our previous results and correct some typos

Scientific paper

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.

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