| 大偏差定理与初值敏感性 |
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| 引用本文： | 牛应轩. 大偏差定理与初值敏感性[J]. 应用数学, 2008, 21(2): 245-250 |
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| 作者姓名： | 牛应轩 |
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| 作者单位： | 皖西学院数理系,安徽,六安,237012 |
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| 基金项目： | Supported by the Natural Science Foundation of the Committee of Education of Anhui Province (KJ2007B123) |
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| 摘 要： | 本文讨论了动力系统的统计性质和动力性质的某些关系.对于紧致度量空间X上的连续自映射f,我们证明了:如果f满足大偏差定理,那么f是初值敏感的当且仅当f不是极小等度连续的.
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| 关 键 词： | 大偏差定理 初值敏感性 拓扑传递 极小的 等度连续的 The large deviations theorem Sensitive dependence on initial conditions Topologically transitive Minimal Equicontinuous 偏差定理 初值敏感性 Initial Conditions Sensitive Dependence Theorem sensitive dependence initial conditions equicontinuous show large deviations theorem continuous map compact metric space stochastic properties dynamical systems paper 等度连续 连续自映射 紧致度量空间 |
| 文章编号： | 1001-9847(2008)02-0245-06 |
| 修稿时间： | 2007-06-12 |
The Large Deviations Theorem and Sensitive Dependence on Initial Conditions |
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| NIU Ying-xuan. The Large Deviations Theorem and Sensitive Dependence on Initial Conditions[J]. Mathematica Applicata, 2008, 21(2): 245-250 |
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| Authors: | NIU Ying-xuan |
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| Abstract: | In this paper,some relations between stochastic and topological properties of dynamical systems are studied.For a continuous map f from a compact metric space X to itself,we show that if f satisfies the large deviations theorem,then f is sensitive dependence on initial conditions if and only if f is not minimally equicontinuous. |
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| Keywords: | The large deviations theorem Sensitive dependence on initial conditions Topologically transitive Minimal Equicontinuous |
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