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February & March  2004, 11(2&3): 325-335. doi: 10.3934/dcds.2004.11.325

Coupled map lattices without cluster expansion

Gerhard Keller 1, and  Carlangelo Liverani 2,

1. 

Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1½, 91054 Erlangen, Germany
2. 

Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, I-00133 Roma, Italy

Received  October 2003 Revised  May 2004 Published  June 2004

We present an approach to the investigation of the statistical properties of weakly coupled map lattices that avoids completely cluster expansion techniques. Although here it is implemented on a simple case we expect similar strategies to be applicable in a much larger class of situations.
Keywords: Coupled map lattice, exponential decay of correlations, transfer operator, spatio-temporal chaos., spectral gap.
Mathematics Subject Classification: 37D20, 37D35, 37A25, 37A60, 82C2.
Citation: Gerhard Keller, Carlangelo Liverani. Coupled map lattices without cluster expansion. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 325-335. doi: 10.3934/dcds.2004.11.325
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