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Published in:
Secants of Trajectories in Dimension Three Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Partial Symmetry Breaking and Heteroclinic Tangencies

Authors : Isabel S. Labouriau, Alexandre A. P. Rodrigues

Published in: Progress and Challenges in Dynamical Systems

Publisher: Springer Berlin Heidelberg

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Abstract

We study some global aspects of the bifurcation of an equivariant family of volume-contracting vector fields on the three-dimensional sphere. When part of the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the symmetry, we investigate the mechanism of the emergence of heteroclinic tangencies coexisting with transverse connections. We find persistent suspended horseshoes accompanied by attracting periodic trajectories with long periods.

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previous chapter Homoclinic Solutions to Infinity and Oscillatory Motions in the Restricted Planar Circular Three Body Problem
next chapter Finding Periodic Orbits in the Hindmarsh-Rose Neuron Model
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Metadata
Title
Partial Symmetry Breaking and Heteroclinic Tangencies
Authors
Isabel S. Labouriau
Alexandre A. P. Rodrigues
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Progress and Challenges in Dynamical Systems

Print ISBN: 978-3-642-38829-3

Electronic ISBN: 978-3-642-38830-9

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-38830-9_17

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