Asymptotic spectral gap for open partially expanding maps

Abstract

We consider a $\mathbb{R}$-extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use a new application of a "global normal form" for the dynamical system, a "semiclassical expression beyond the Ehrenfest time" that expresses the transfer operator at large time as a sum over rank one operators (each is associated to one orbit). In this paper we establish the validity of the so-called "diagonal approximation" up to twice the local Ehrenfest time.

51 pages

References in corpus (2)

• Experimental Observation of the Spectral Gap in Microwave n-Disk Systems
• Exponential mixing for generic volume-preserving Anosov flows in dimension three