99-224 Torsten Fischer
Coupled Map Lattices with Asynchronous Updatings (578K, postscript) Jun 10, 99
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Abstract. We consider on $M= (S^1)^{\Z^d}$ a family of continuous local updatings, of finite range type or Lipschitz-continuous in all coordinates with summable Lipschitz-constants. We show that the infinite-dimensional dynamical system with independent identically Poisson-distributed times for the individual updatings is well-defined. In the setting of analytically coupled uniformly expanding, analytic circle maps with weak, exponentially decaying interaction, we define transfer operators for the infinite-dimensional system, acting on Banch-spaces that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. We prove existence and uniqueness (in the considered Banach space) of a probability measure and its exponential decay of correlations.

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