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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.
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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