# A thermodynamic approach to two-variable Ruelle and Selberg zeta functions via the Farey map - Mathematics > Dynamical Systems

A thermodynamic approach to two-variable Ruelle and Selberg zeta functions via the Farey map - Mathematics > Dynamical Systems - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: In this paper we consider the transfer operator approach to the Ruelle andSelberg zeta functions associated to continued fractions transformations andthe geodesic flow on the full modular surface. We extend the results by Ruelleand Mayer to two-variable zeta functions, $\zetaq,z$ and $Zq,z$. The $q$variable plays the role of the inverse temperature and the introduction of the-geometric variable- $z$ is essential in the tentative to provide a generalapproach, based on the Farey map, to the correspondence between the analyticproperties of the zeta functions themselves, the spectral properties of a classof generalised transfer operators and the theory of a generalisation of thethree-term functional equations studied by Lewis and Zagier. The first step inthis direction is a detailed study of the spectral properties of a family ofsigned transfer operators $\PP^{\pm} {q}$ associated to the Farey map.

Autor: Claudio Bonanno, Stefano Isola

Fuente: https://arxiv.org/

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