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

F. Bonetto, A. Kupiainen, J. L. Lebowitz

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We study a d-dimensional coupled map. lattice consisting of hyperbolic total automorphisms (Arnold cat maps) that are weakly coupled by an analytic map. We construct the Sinai-Ruelle-Bowen measure for this system and study its marginals on the tori. We prove that they are absolutely continuous with respect to Lebesgue measure if and only if the coupling satisfies a non-degeneracy condition.
Original languageEnglish
JournalErgodic Theory and Dynamical Systems
Issue number1
Pages (from-to)59-88
Number of pages30
Publication statusPublished - 2005
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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