Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cro...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2014-03, Vol.29 (1), p.108-118
Main Authors: Xu, Yan-cong, Geng, Feng-jie
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-014-3016-6