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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 $$u'= -J\nabla H(u)+ p(\varepsilon, t,u)$$. 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:
 70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics 70K44 Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics 70K50 Bifurcations and instability for nonlinear problems in mechanics
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