Bifurcation of multi-bump homoclinics in systems with normal and slow variables

Abstract

Bifurcation of multi-bump homoclinics is studied for a pair of ordinary differential equations with periodic perturbations when the first unperturbed equation has a manifold of homoclinic solutions and the second unperturbed equation is vanishing. Such ordinary differential equations often arise in perturbed autonomous Hamiltonian systems.

Keywords

• homoclinics
• averaging
• bifurcation.