A computer-assisted proof of the existence of Smale horseshoe for the folded-towel map

被引：0

作者：

Gierzkiewicz, Anna ^{[1
]}

机构：

[1] Agr Univ Krakow, Dept Appl Math, Ul Balicka 253c, PL-30198 Krakow, Poland

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 96卷

关键词：

Computer assisted proof; Symbolic Dynamics; Hyperbolicity; Folded towel map; COVERING RELATIONS; HYPERCHAOS;

D O I：

10.1016/j.cnsns.2020.105680

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper contains a rigorous proof of existence of symbolic dynamics chaos in the generalized Henon map's 4th iterate H-4, which was conjectured in the paper A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System of Li and Yang, 2007. We prove also the uniform hyperbolicity of the invariant set with symbolic dynamics. The proofs are computer assisted with the use of C++ library CAPD for interval arithmetic, differentiation and integration. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：9

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