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

Published online by Cambridge University Press:  22 December 2004

F. BONETTO ,
A. KUPIAINEN  and
J. L. LEBOWITZ
F. BONETTO
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: bonetto@math.gatech.edu)
A. KUPIAINEN
Affiliation:
Department of Mathematics, Helsinki University, PO Box 4, Helsinki 00014, Finland (e-mail: antti.kupiainen@helsinki.fi)
J. L. LEBOWITZ
Affiliation:
Department of Mathematics and Physics, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: lebowitz@fermat.rutgers.edu)
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Abstract

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We study a d-dimensional coupled map lattice consisting of hyperbolic toral 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 1 , February 2005 , pp. 59 - 88
Copyright
2004 Cambridge University Press