95-142 Stefano Isola

Dynamical zeta functions for non-uniformly hyperbolic transformations. (46K, Plain-Tex) Mar 9, 95

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Abstract. We consider a class of maps $f$ of $[0,1]$ which are expanding everywhere but at a fixed point, which we allow to be neutral. We follow two parallel approaches: 1) using an induced version $g$ of the map $f$ we are able to relate the analytic properties of the dynamical zeta functions associated to $f$ and $g$ and the spectral properties of the corresponding transfer operators; 2) using a suitable piecewise affine approximation $\hf$ of the map $f$ we obtain information on the behaviour of the corresponding zeta functions in the whole complex plane. One result is that if $f$ has a neutral fixed point then its zeta function extends meromorphically in the entire complex plane with a cross cut along the ray $(1,+\infty)$.

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