Resonant Homoclinic Flips Bifurcation in Principal Eigendirections

Abstract EN

A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered.

By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation.

A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits.

We also locate their bifurcation surfaces in certain regions.