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Article Dans Une Revue Communications in Mathematical Physics Année : 2017

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

Frédéric Faure
Tobias Weich
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Résumé

We consider a 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.

Dates et versions

hal-01656370 , version 1 (05-12-2017)

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Citer

Frédéric Faure, Tobias Weich. Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. Communications in Mathematical Physics, 2017, 356 (3), pp.755 - 822. ⟨10.1007/S00220-017-3000-0⟩. ⟨hal-01656370⟩
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