Absolute continuity of projected SRB measures of coupled Arnold cat map lattices

Details Absolute continuity of projected SRB measures of coupled Arnold cat map lattices Absolute continuity of projected SRB measures of coupled Arnold cat map lattices

2003-10-08

arxiv.org/abs/nlin/0310009v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

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.

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