| Shadowing and Inverse Shadowing for C^1 Endomorphisms |
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| 引用本文： | Yu Jun ZHU Jin Lian ZHANG Lian Fa HE. Shadowing and Inverse Shadowing for C^1 Endomorphisms[J]. 数学学报(英文版), 2006, 22(5): 1321-1328. DOI: 10.1007/s10114-005-0739-6 |
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| 作者姓名： | Yu Jun ZHU Jin Lian ZHANG Lian Fa HE |
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| 作者单位： | [1]College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China [2]School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China |
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| 基金项目： | Research supported by the National Natural Science Foundation of China （10371030）, the Tian Yuan Mathematical Foundation of China （10426012） and the Doctoral Foundation of Hebei Normal University （L2003B05）. |
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| 摘 要： | In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.
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| 关 键 词： | 逆转阴影 自同态 双曲线设置 数学分析 |
| 收稿时间： | 2005-11-25 |
| 修稿时间： | 2005-11-25 |
Shadowing and Inverse Shadowing for C 1 Endomorphisms |
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| Yu Jun Zhu,Jin Lian Zhang,Lian Fa He. Shadowing and Inverse Shadowing for C 1 Endomorphisms[J]. Acta Mathematica Sinica(English Series), 2006, 22(5): 1321-1328. DOI: 10.1007/s10114-005-0739-6 |
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| Authors: | Yu Jun Zhu Jin Lian Zhang Lian Fa He |
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| Affiliation: | (1) College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China;(2) School of Mathematical Sciences, Peking University, Bejing 100871, P. R. China;(3) College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China |
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| Abstract: | In this paper, we consider the shadowing and the inverse shadowing properties for C 1 endomorphisms. We show that near a hyperbolic set a C 1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also “uniform” with respect to C 1 perturbation. Research supported by the National Natural Science Foundation of China (10371030), the Tian Yuan Mathematical Foundation of China (10426012) and the Doctoral Foundation of Hebei Normal University (L2003B05) |
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| Keywords: | shadowing property inverse shadowing property endomorphism Hyperbolic set |
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