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Zbl 1039.70012
Henrard, Marc; Zanolin, Fabio
Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
(English)
[J] J. Math. Anal. Appl. 277, No. 1, 79-103 (2003). ISSN 0022-247X

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.
[Václav Burjan (Praha)]
MSC 2000:
*70H09 Perturbation theories
70K44 Homoclinic and heteroclinic trajectories
70K50 Transition to stochasticity (general mechanics)

Keywords: homoclinic trajectory; Carathéodory function; existence; $T$-periodic solution; time map

Cited in: Zbl 1151.34050

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