versione YYYYYY

**Author**:
F.Bonetto, P.Falco, A.Giuliani

**Title**: *
Analyticity of the SRB measure of a lattice of coupled Anosov
diffeomorphisms of the torus*

**Abstract:**
We consider the ``thermodynamic limit'' of a
*d*-dimensional lattice of hyperbolic dynamical systems on the 2-torus,
interacting via weak and nearest neighbor coupling. We prove that the
SRB measure is analytic in the strength of the coupling. The proof is
based on symbolic dynamics techniques that allow us to map the SRB
measure into a Gibbs measure for a spin system on a
*(d+1)*-dimensional lattice. This Gibbs measure can be studied by an
extension (* decimation *) of the usual ``cluster expansion''
techniques.

**E-mail:**
bonetto@math.gatech.edu

falco@mat.uniroma1.it

alessandro.giuliani@roma1.infn.it