Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for κ-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-SchrSdinger Equation  

作　　者：Fu-qi Yin Sheng-fan Zhou 

机构地区：[1]Department of Mathematics, Xiangtan University, Xiangtan 411105, China [2]Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

出　　处：《Acta Mathematicae Applicatae Sinica》2006年第3期469-486,共18页应用数学学报（英文版）

基　　金：Supported by thc National Natural Science Foundation of China （No.10471086）. Acknowledgements. The authors thank the reviewers very much for their useful suggestions and comments.

摘　　要：In this paper, we establish the existence of a global attractor for a coupled κ-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-SchrSdinger Equation. An estimate of the upper bound of the Kohnogorov 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 .In this paper, we establish the existence of a global attractor for a coupled κ-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-SchrSdinger Equation. An estimate of the upper bound of the Kohnogorov 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 .

关 键 词：Global attractor lattice dynamical system element decomposition Kolmogorov ε-entropy upper semicontinuity 

分 类 号：O17[理学—数学]