Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows

Details Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows

2011-04-05

arxiv.org/abs/1104.0732v1

Mathematics

Dynamical Systems

Scientific paper

For Anosov flows on compact Riemann manifolds we study the rate of decay along the flow of diameters of balls $B^s(x,\ep)$ on local stable manifolds at Lyapunov regular points $x$. We prove that this decay rate is similar for all sufficiently small values of $\epsilon > 0$. From this and the main result in \cite{kn:St1}, we derive strong spectral estimates for Ruelle transfer operators for contact Anosov flows with Lipschitz local stable holonomy maps. These apply in particular to geodesic flows on compact locally symmetric manifolds of strictly negative curvature. As is now well known, such spectral estimates have deep implications in some related areas, e.g. in studying analytic properties of Ruelle zeta functions and partial differential operators, asymptotics of closed orbit counting functions, etc.

Affiliated with

Also associated with

No associations

Rating

Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows 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 Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-320796