# Some Topological Properties of Lattice Dynamical Systems

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## **Abstract**

Phenomenological models of motions in media with dissipation in the form of lattices of coupled ordinary differential equations or maps appeared about 50 years ago and since then play an important role in study of dynamical properties of systems in material science, fluid dynamics, chemistry, image processing, biology, etc [1]. We will call them Lattice Dynamical Systems (LDS), see below. A special class of LDS, the so called Coupled Map Lattices (CML), has been introduced almost simultaneously in [2, 3, 4, 5] and, mainly because of convenience of numerical simulations, became a basic model in the .eld [6]. Beginning with [7], many rigorous mathematical results have been obtained concerning topological and ergodic features of LDS and CML.

## Keywords

Topological Property Periodic Point Travel Wave Solution Homoclinic Orbit Topological Entropy## Preview

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