# American Institute of Mathematical Sciences

March  2004, 11(2&3): 581-598. doi: 10.3934/dcds.2004.11.581

## Birkhoff cones, symbolic dynamics and spectrum of transfer operators

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

Received  March 2003 Revised  April 2004 Published  June 2004

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.
Citation: Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581
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