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Exponential attractors for second order lattice dynamical systems. (English) Zbl 1167.37037
Lattice dynamical systems are infinite systems of ODEs or difference equations, indexed by points in a lattice, such as the k-dimensional integer lattice k . In the article [J. Math. Anal. Appl. 339, No. 1, 217–224 (2008; Zbl 1127.37051)], the author had introduced the exponential attractors for LDS, where a first order system has been presented. Here he proves the existence of an exponential attractors for the solution semigroup of a second order LDS acting on an closed bounded positively invariant set in the infinite dimensional Hilbert space l 2 ×l 2 .

MSC:
37L30Attractors and their dimensions, Lyapunov exponents
37L60Lattice dynamics (infinite-dimensional dissipative systems)