| Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for κ-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-SchrSdinger Equation |
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| 作者姓名： | Fu-qi Yin Sheng-fan Zhou |
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| 作者单位： | [1]Department of Mathematics, Xiangtan University, Xiangtan 411105, China [2]Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China |
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| 基金项目： | 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. |
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| 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 .
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| 关 键 词： | 整体吸引子 晶格动力系统 元素分解 Kolmogorov ε-熵 上准连续性 |
| 收稿时间： | 2005-06-01 |
| 修稿时间： | 2005-06-012006-02-04 |
Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for k-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-Schrödinger Equation |
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| Fu-qi Yin Sheng-fan Zhou.Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for k-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-Schrödinger Equation[J].Acta Mathematicae Applicatae Sinica,2006,22(3):469-486. |
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| Authors: | Fu-qi Yin Sheng-fan Zhou |
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| Institution: | (1) Department of Mathematics, Xiangtan University, Xiangtan, 411105, China;(2) Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China |
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| Abstract: | Abstract
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-Schr?dinger 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 .
Supported by the National Natural Science Foundation of China (No.10471086). |
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| Keywords: | Global attractor lattice dynamical system element decomposition Kolmogorov ε -entropy upper semicontinuity |
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