Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
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.
scientific article; zbMATH DE number 1895742
scientific article