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Transversal homoclinics in nonlinear systems of ordinary differential equations. (English) Zbl 0985.37017
Summary: Bifurcation of transversal 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.
MSC:
37C29 Homoclinic and heteroclinic orbits for dynamical systems
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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