03-391 V. Baladi, E.R. Pujals, and M. Sambarino

Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting (147K, AMS TeX) Aug 29, 03

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Abstract. We consider a real-analytic compact surface diffeomorphism for which the tangent space over the nonwandering set admits a dominated splitting. We study the Ruelle-Fredholm dynamical determinant d(z). By combining previous work of Pujals and Sambarino on C2 surface diffeomorphisms with, on the one hand, results of Rugh on hyperbolic analytic maps, and on the other, our two-dimensional version of Rugh's analysis of one-dimensional analytic dynamics with neutral fixed points, we prove that df(z) is either entire or a holomorphic function in a (possibly multiply) slit plane.

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