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Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting

Viviane Baladi·Enrique R. Pujals·Martin Sambarino
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Abstract

We study the Ruelle dynamical determinant of a real analytic diffeomorphism on a compact surface, assuming that the tangent space over the nonwandering set admits a dominated splitting. Combining previous work of Pujals and Sambarino with methods introduced by Rugh, we show that the determinant is either entire or holomorphic in a (possibly multiply) slit plane.

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Viviane Baladi, Enrique R. Pujals, Martin Sambarino. 2003-08-29. Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting. https://arxiv.org/abs/math/0307045

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