Construction of codimension one homoclinic cycles
| Authors |
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| Publication date | 2014 |
| Journal | Dynamical Systems |
| Volume | Issue number | 29 | 1 |
| Pages (from-to) | 133-151 |
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| Abstract |
We give an explicit construction of families of D-m-equivariant polynomial vector fields in R-4 possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m equal to a multiple of 4, where the bifurcations form an open problem. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1080/14689367.2013.860085 |
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