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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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