Lifted Lattices, Hyperbolic Structures, and Topological Disorders in Coupled Map Lattices

Abstract

A lifted lattice is introduced to characterize the stability and hyperbolicity of solutions and to study the existence of topological disorders and chaos in a given coupled map lattice. Time almost-periodic coupled map lattices are also considered through the associated lifted lattices. In particular, the existence of almost-periodic solutions in a discrete-time almost-periodic Nagumo equation is proved.