Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus

Details Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus

2003-12-10

arxiv.org/abs/math-ph/0312032v1

Physics

Mathematical Physics

28 pages, 2 figures

Scientific paper

10.1063/1.1768620

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.

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