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Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps

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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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Authors and Affiliations

  1. Institut Fourier, UMR 5582, Université Grenoble Alpes, 100 rue des Maths, BP74, 38402, St Martin d’Hères, France

    Frédéric Faure

  2. Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Tobias Weich

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  1. Frédéric Faure
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  2. Tobias Weich
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Correspondence to Frédéric Faure.

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Communicated by C. Liverani

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Faure, F., Weich, T. Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. Commun. Math. Phys. 356, 755–822 (2017). https://doi.org/10.1007/s00220-017-3000-0

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