Rn上返回排斥子的Lipschitz结构稳定性
The Lipschitz Perturbations of Snapback Re-pellers in Rn
DOI: 10.12677/AAM.2022.1112891, PDF,    科研立项经费支持
作者: 陈员龙, 吴小英*：广东金融学院金融数学与统计学院，广东 广州
关键词: 混沌动力系统；Lipschitz扰动；返回排斥子；结构稳定性；Chaotic Dynamical System； Lipschitz Perturbations； Snapback Repellers； Structural Stability
摘要: 本文研究欧氏空间上返回排斥子的Lipschitz扰动。设f，g是欧氏空间Rn上的连续自映射，如果f具有返回排斥子且g是f的Lipschitz小扰动，则g也有返回排斥子。因此欧氏空间Rn上的返回排斥子是Lipschitz结构稳定的。
Abstract: This note is concerned with the effect of small Lipschitz perturbations of a discrete dynamical sys-tem in Rn. Let f, g be continuous map from Rn into itself. If f has snap-back repellers and g is a small Lipschitz perturbations of f, then g has snap-back repellers. In addition, the snap-back repellers are Lipschitz structural stability in Rn.
文章引用：陈员龙, 吴小英. Rn上返回排斥子的Lipschitz结构稳定性[J]. 应用数学进展, 2022, 11(12): 8426-8430. https://doi.org/10.12677/AAM.2022.1112891

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