**Author**: Federico Bonetto. Antti Kupiainen and Joel Lebowitz

**Title**: *
Absolute continuity of projected SRB measures of coupled Arnold
cat map lattices*

**Abstract:**
We study a d-dimensional coupled map lattice consisting of
hyperbolic toral automorphisms
(Arnold cat maps) that are weakly coupled by an analytic
coupling map. We construct the Sinai-Ruelle-Bowen measure
for this system and study
its marginals on the tori. We prove they are absolutely continuous
with respect to the Lebesgue measure if and only if
the coupling satisfies a nondegeneracy condition.

**Key words: **
dynamical systems, perturbation theory, projected measure,
absolute continuity

** APS-PACS: **
47.52.+j, 05.45.+b, 05.70.Ln, 47.70.-n

F. Bonetto

School of Mathematics

Georgia Institute of Technology

Atlanta, GA 30332

bonetto@math.gatech.edu

A. Kupiainen

Department of Mathematics,

Helsinki University

P.O Box 4

Helsinki 00014

Finland

ajkupiai@cc.helsinki.edu

J.L. Lebowitz

Department of Mathematics and Physics,

Rutgers University

New Brunswick, NJ 08903

lebowitz@math.rutgers.edu