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We consider Kolmogorov’s ε-entropy of the global attractor for first and second order dissipative lattice dynamical systems. By using the element decomposition and the covering property of a polyhedron by balls of radii ε in the finite dimensional space, we obtain an estimate of the upper bound for Kolmogorov’s ε-entropy of the global attractor.

In this paper, we consider the existence of a global periodic attractor for a strongly damped nonlinear wave equation with time-periodic driving force under homogeneous Dirichlet boundary condition. It is proved that in certain parameter region, for arbitrary time-periodic driving force, the system has a unique periodic solution attracting any bounded set exponentially. This implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of global periodic attractor of the usual damped and driven wave equations.

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