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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Acknowledgements
The authors would like to thank Maria Carvalho for helpful discussions.
CMUP is supported by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the Fundação para a Ciência e a Tecnologia (FCT) under the project PEst-C/MAT/UI0144/2011. A.A.P. Rodrigues was supported by the grant SFRH/BPD/84709/2012 of FCT.
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Labouriau, I.S., Rodrigues, A.A.P. (2013). Partial Symmetry Breaking and Heteroclinic Tangencies. In: Ibáñez, S., Pérez del Río, J., Pumariño, A., Rodríguez, J. (eds) Progress and Challenges in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38830-9_17
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DOI: https://doi.org/10.1007/978-3-642-38830-9_17
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