FM 2003-10;

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