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arXiv · 1504.06728

Asymptotic spectral gap for open partially expanding maps

Frédéric Faure·Tobias Weich
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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.

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Frédéric Faure, Tobias Weich. 2017-08-10. Asymptotic spectral gap for open partially expanding maps. https://arxiv.org/abs/1504.06728

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