Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting

Details Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting Dynamical zeta functions for analytic surface diffeomorphisms with dominated splitting

2003-07-03

arxiv.org/abs/math/0307045v2

Mathematics

Dynamical Systems

Revised version, some mistakes corrected (e.g. in Section 3)

Scientific paper

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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