On the distribution of periodic orbits

Details On the distribution of periodic orbits On the distribution of periodic orbits

2009-01-14

arxiv.org/abs/0901.2139v1

Mathematics

Dynamical Systems

Scientific paper

Let $f:M\to M$ be a $C^{1+\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\Lambda\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f|\Lambda$. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphisms. We show that the topological pressure $P_{\rm top}(\varphi)$ can be computed by the values of the potential $\varphi$ on the expanding periodic orbits and also that every hyperbolic ergodic invariant measure is well-approximated by expanding periodic orbits. Moreover, we prove that certain equilibrium states are Bowen measures. Finally, we derive a large deviation result for the periodic orbits whose time averages are apart from the space average of a given hyperbolic invariant measure.

Affiliated with

Also associated with

No associations

Rating

On the distribution of periodic orbits 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 On the distribution of periodic orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the distribution of periodic orbits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-589164