关于吸引子的某些性质 |
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引用本文: | 黄土森.关于吸引子的某些性质[J].数学学报,1999,42(5):873-876. |
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作者姓名: | 黄土森 |
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作者单位: | 宁波大学管理学系!宁波,315211 |
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摘 要: | Conley在1]中讨论拓扑空间X上动力系统的吸引子——排斥子对时,给出了吸引子存在的两个充分条件.本文证明这两个条件实际上也是必要的,进而证明Conley所定义的吸引子是渐近稳定的.
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关 键 词: | 集合极限集 吸引子 排斥子 延伸集 延伸极限集 稳定性 |
Some Properties of Attractors |
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Institution: | Huang Tusen (Department of Mandgement, Ningbo University, Ningbo 315211, P. R. China) |
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Abstract: | Conley gave two sufficient conditions of the existence of an attractor when he discussed attrastor-repeller pairs of a dynamical system on a topological space X in 1]. In this paper, we prove that these two sufficient conditions are, in fact, necessary. Further, we prove that any attractor defined by Conley must be asymptotically stable. |
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