- Construction of codimension one homoclinic cycles
- Dynamical Systems
- Volume | Issue number
- 29 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
- 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.
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