| Kolmogorov＇s ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems |
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| 引用本文： | Sheng Fan ZHOU Qiu Li JIA Wei SHI. Kolmogorov＇s ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems[J]. 数学学报(英文版), 2007, 23(2): 313-320. DOI: 10.1007/s10114-005-0871-3 |
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| 作者姓名： | Sheng Fan ZHOU Qiu Li JIA Wei SHI |
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| 作者单位： | [1]Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China [2]Department of Mathematics and Physics, He ＇nan University of Science and Technology, Luoyang 471003, P. R. China [3]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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| 基金项目： | This work is supported bythe National Natural Science Foundation of China under Grants 10471086, and the Science Foundation of He＇nan Unversity of Science and Technology under Grant 2006QN024 |
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| 摘 要： | We obtain an estimate of the upper bound for Kolmogorov＇s ε-entropy for the bounded sets with small ＂tail＂ in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov＇s ε-entropy of the global attractor for lattice systems.
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| 关 键 词： | 耗散网格系统 离散空间 全局吸引子 科尔莫戈罗夫ε-熵 |
| 收稿时间： | 2004-10-28 |
| 修稿时间： | 2004-10-282005-03-22 |
Kolmogorov’s ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems |
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| Sheng Fan Zhou,Qiu Li Jia,Wei Shi. Kolmogorov’s ε-Entropy of Bounded Sets in Discrete Spaces and Attractors of Dissipative Lattice Systems[J]. Acta Mathematica Sinica(English Series), 2007, 23(2): 313-320. DOI: 10.1007/s10114-005-0871-3 |
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| Authors: | Sheng Fan Zhou Qiu Li Jia Wei Shi |
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| Affiliation: | (1) Department of Applied Mathematics, Shanghai Normal University,, Shanghai 200234, P. R. China;(2) Department of Mathematics and Physics, He’nan University of Science and Technology, Luoyang 471003, P. R. China;(3) Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | We obtain an estimate of the upper bound for Kolmogorov’s ε-entropy for the bounded sets with small “tail” in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov’s ε-entropy of the global attractor for lattice systems. This work is supported by the National Natural Science Foundation of China under Grants 10471086, and the Science Foundation of He’nan Unversity of Science and Technology under Grant 2006QN024 |
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| Keywords: | Kolmogorov’ s ε -entropy discrete space dissipative lattice system global attractor |
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