Robust entropy expansiveness implies generic domination

Details Robust entropy expansiveness implies generic domination Robust entropy expansiveness implies generic domination

2009-03-17

arxiv.org/abs/0903.2948v3

Mathematics

Dynamical Systems

24 pages

Scientific paper

Let $f: M \to M$ be a $C^r$-diffeomorphism, $r\geq 1$, defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$, and let $H(p)$ be the homoclinic class associated to the hyperbolic periodic point $p$. We prove that if there exists a $C^1$ neighborhood $\mathcal{U}$ of $f$ such that for every $g\in {\mathcal U}$ the continuation $H(p_g)$ of $H(p)$ is entropy-expansive then there is a $Df$-invariant dominated splitting for $H(p)$ of the form $E\oplus F_1\oplus... \oplus F_c\oplus G$ where $E$ is contracting, $G$ is expanding and all $F_j$ are one dimensional and not hyperbolic.

Affiliated with

Also associated with

No associations

Rating

Robust entropy expansiveness implies generic domination does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Robust entropy expansiveness implies generic domination, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Robust entropy expansiveness implies generic domination will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-491334