Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting
Viviane Baladi, Enrique R. Pujals, Martin Sambarino
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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