A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem

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 n...

Full description

Bibliographic Details
Main Authors:	Xuhua Cheng, Zhikun She
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2015/965829

id	doaj-08034d8a884d4484816dc5d557e6b2c7
record_format	Article
spelling	doaj-08034d8a884d4484816dc5d557e6b2c72020-11-24T20:51:46ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/965829965829A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body ProblemXuhua Cheng0Zhikun She1SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, ChinaSKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, ChinaIt 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.http://dx.doi.org/10.1155/2015/965829
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xuhua Cheng Zhikun She
spellingShingle	Xuhua Cheng Zhikun She A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem Abstract and Applied Analysis
author_facet	Xuhua Cheng Zhikun She
author_sort	Xuhua Cheng
title	A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
title_short	A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
title_full	A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
title_fullStr	A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
title_full_unstemmed	A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
title_sort	note on the existence of a smale horseshoe in the planar circular restricted three-body problem
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2015-01-01
description	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.
url	http://dx.doi.org/10.1155/2015/965829
work_keys_str_mv	AT xuhuacheng anoteontheexistenceofasmalehorseshoeintheplanarcircularrestrictedthreebodyproblem AT zhikunshe anoteontheexistenceofasmalehorseshoeintheplanarcircularrestrictedthreebodyproblem AT xuhuacheng noteontheexistenceofasmalehorseshoeintheplanarcircularrestrictedthreebodyproblem AT zhikunshe noteontheexistenceofasmalehorseshoeintheplanarcircularrestrictedthreebodyproblem
_version_	1716801330722373632

A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem

Similar Items