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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.

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