 95142 Stefano Isola
 Dynamical zeta functions for nonuniformly hyperbolic transformations.
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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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