Keller G, Künzle M (1992)
Publication Type: Journal article, Original article
Publication year: 1992
Publisher: Cambridge University Press (CUP)
Book Volume: 12
Pages Range: 297-318
Journal Issue: 2
DOI: 10.1017/S0143385700006763
Let L denote a finite or infinite one-dimensional lattice. To each lattice site is attached a copy of a dynamical system with phase space [0, 1] and dynamics described by a transformation τ: [0, 1] → [0, 1], which is the same on each component. Denote the direct product of these identical systems by T: X → X where X = [0, 1]L. From this product system we obtain a coupled map lattice (CML) Sε: X → X, if we introduce some interaction between the components, e.g. by averaging between nearest neighbours. The strength of the coupling depends upon some parameter ε.
For a broad class of piecewise expanding single-component-transformations τ we study such systems via their transfer operators and treat the coupled system as a perturbation of the uncoupled one. This yields existence and stability results for T-invariant measures with absolutely continuous finite-dimensional marginals.
APA:
Keller, G., & Künzle, M. (1992). Transfer operators for coupled map lattices. Ergodic Theory and Dynamical Systems, 12(2), 297-318. https://doi.org/10.1017/S0143385700006763
MLA:
Keller, Gerhard, and Martin Künzle. "Transfer operators for coupled map lattices." Ergodic Theory and Dynamical Systems 12.2 (1992): 297-318.
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