Torsten Fischer
Coupled Map Lattices with Asynchronous Updatings
(578K, postscript)
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.