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Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems. (English) Zbl 1039.70012
The authors study the perturbed plane differential system u ' =-JH(u)+p(ε,t,u). Here t is a variable, p is Carathéodory function, T is periodic in variable t, and j is a symplectic matrix. T-periodic functions are looked for. Theorems are proved which give conditions for the existence of T-periodic solution. Some properties of the time map are discussed, and an application of periodic solutions close to the homoclinic ones is studied.

70H09Perturbation theories (mechanics of particles and systems)
70K44Homoclinic and heteroclinic trajectories (nonlinear dynamics)
70K50Transition to stochasticity (general mechanics)