A note on the existence of a smale horseshoe in the planar circular restricted three-body problem

Xuhua Cheng; Zhikun She

doi:10.1155/2015/965829

A note on the existence of a smale horseshoe in the planar circular restricted three-body problem

Xuhua Cheng^*
, Zhikun She

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.

源语言	英语
文章编号	965829
期刊	Abstract and Applied Analysis
卷	2015
DOI	https://doi.org/10.1155/2015/965829
出版状态	已出版 - 2015

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abstract = "It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.",

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AB - It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits. Since the standard Smale-Birkhoff theorem cannot be directly applied to indicate the chaotic dynamics of the Smale horseshoe type, we in this note alternatively apply the Conley-Moser conditions to analytically prove the existence of a Smale horseshoe in this classical restricted three-body problem.

UR - https://www.scopus.com/pages/publications/84926500618

U2 - 10.1155/2015/965829

DO - 10.1155/2015/965829

M3 - 文章

AN - SCOPUS:84926500618

SN - 1085-3375

VL - 2015

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

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A note on the existence of a smale horseshoe in the planar circular restricted three-body problem

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