Upper semicontinuity and Kolmogorov ε-entropy of global attractor for k-dimensional lattice dynamical system corresponding to Klein-Gordon- Schrödinger equation

In this paper, we establish the existence of a global attractor for a coupled k-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-Schrödinger Equation. An estimate of the upper bound of the Kolmogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented . © 2006 Springer-Verlag Berlin Heidelberg.