An example of a resonant homoclinic loop of infinite cyclicity
- Turaev, Dmitry
2010 Mathematics Subject Classification
- 37G20 34C07 34C37
- codimension-3 homoclinic bifurcation, invariant manifold, swallow tail, limit cycle
We describe a codimension-3 bifurcational surface in the space of 𝐶𝑟-smooth (𝑟 ≥ 3) dynamical systems (with the dimension of the phase space equal to 4 or higher) which consists of systems which have an attractive two-dimensional invariant manifold with an infinite sequence of periodic orbits of alternating stability which converge to a homoclinic loop.