WIAS Preprint No. 838, (2003)

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.

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