Mathematics – Dynamical Systems
Scientific paper
2010-05-05
Mathematics
Dynamical Systems
Scientific paper
We obtain a large deviation function for the stationary measures of twisted Brownian motions associated to the Lagrangians $L_{\lambda}(p,v)=\frac{1}{2}g_{p}(v,v)- \lambda\omega_{p}(v)$, where $g$ is a $C^{\infty}$ Riemannian metric in a compact surface $(M,g)$ with nonpositive curvature, $\omega$ is a closed 1-form such that the Aubry-Mather measure of the Lagrangian $L(p,v)=\frac{1}{2}g_{p}(v,v)-\omega_{p}(v)$ has support in a unique closed geodesic $\gamma$; and the curvature is negative at every point of $M$ but at the points of $\gamma$ where it is zero. We also assume that the Aubry set is equal to the Mather set. The large deviation function is of polynomial type, the power of the polynomial function depends on the way the curvature goes to zero in a neighborhood of $\gamma$. This results has interesting counterparts in one-dimensional dynamics with indifferent fixed points and convex billiards with flat points in the boundary of the billiard. A previous estimate by N. Anantharaman of the large deviation function in terms of the Peierl's barrier of the Aubry-Mather measure is crucial for our result.
Lopes Artur O.
Ruggiero Rafael O.
No associations
LandOfFree
Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics 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 Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-438028