Birkhoff cones, symbolic dynamics and spectrum of transfer operators

Frédéric Naud

doi:10.3934/dcds.2004.11.581

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2004, Volume 11, Issue 2&3: 581-598. Doi: 10.3934/dcds.2004.11.581

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Birkhoff cones, symbolic dynamics and spectrum of transfer operators

Frédéric Naud^1,

1.
Laboratoire Bordelais d'Analyse et Géométrie, Université Bordeaux 1, 33405 Talence

Received: February 28, 2003

Revised: March 31, 2004

Published: August 2004

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Abstract

In this paper, we give an alternative proof of the classical Ruelle-Perron-Frobenius theorem in the general setup of subshifts of finite type using Birkhoff cones and Hilbert metrics. This approach yields an explicit estimate of the spectral gap of transfer operators and can be applied to compute estimates of the rate of decay of correlations and the analytic continuation of zeta functions.

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Mathematics Subject Classification: 37C30, 37B10.

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