Birkhoff cones, symbolic dynamics and spectrum of transfer operators
Frédéric Naud
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.
keywords: decay of correlations. Birkhoff cones Hilbert metrics transfer operators symbolic dynamics
The Ruelle spectrum of generic transfer operators
Frédéric Naud
We define a natural space of transfer operators related to holomorphic contraction systems. We show that the classical upper bounds on the Ruelle eigenvalue sequence are optimal for a dense set of transfer operators. A similar statement is derived for Perron-Frobenius operators related to uniformly expanding piecewise real analytic interval maps. The proof is based on potential theory.
keywords: decay of correlation Perron-Frobenius operators potential theory. Ruelle eigenvalues holomorphic function spaces Transfer operators

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