Abdallah, Ahmed Y. Exponential attractors for second order lattice dynamical systems. (English) Zbl 1167.37037 Commun. Pure Appl. Anal. 8, No. 3, 803-813 (2009). Lattice dynamical systems are infinite systems of ODEs or difference equations, indexed by points in a lattice, such as the \(k\)-dimensional integer lattice \(\mathbb{Z}^k\). 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 \(l^2\times l^2\). Reviewer: Boris V. Loginov (Ul’yanovsk) Cited in 1 ReviewCited in 17 Documents MSC: 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems Keywords:lattice dynamical systems; squeezing property; exponential attractor Citations:Zbl 1127.37051 PDFBibTeX XMLCite \textit{A. Y. Abdallah}, Commun. Pure Appl. Anal. 8, No. 3, 803--813 (2009; Zbl 1167.37037) Full Text: DOI