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Topological properties of linearly coupled expanding map lattices. (English) Zbl 0983.37100

This paper deals with some topological features of one-dimensional coupled map lattices (CML) with expanding maps of an interval and convolution-type coupling. The authors show the existence of an invariant set in which the symbolic dynamics is described by the product of local symbolic systems. Provided that the local symbolic dynamics is nontrivial they show that for any \(v\in\mathbb{R}\), the travelling wave configurations of velocity \(v\) are dense, in the uniform topology, in the hyperbolic subset. Moreover, the authors address the question of the existence of a convolution renormalization map for some class of coupled map lattices.

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37B25 Stability of topological dynamical systems
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