Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem
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Periodic solutions, Poincaré-Birkhoff, nonlinear dynamicsAbstrakt
We prove the existence of periodic solutions for a planar non-autonomous Hamiltonian system which is a small perturbation of an autonomous system, in the presence of a non-isochronous period annulus. To this aim we use the Poincaré-Birkhoff fixed point theorem, even if the boundaries of the annulus are neither assumed to be invariant for the Poincaré map, nor to be star-shaped. As a consequence, we show how to deal with the problem of bifurcation of subharmonic solutions near a given nondegenerate periodic solution. In this framework, we only need little regularity assumptions, and we do not need to introduce any Melnikov type functions.Pobrania
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2012-04-23
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FONDA, Alessandro, SABATINI, Marco & ZANOLIN, Fabio. Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the
Poincaré-Birkhoff theorem. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 40, nr 1, s. 29–52. [udostępniono 22.7.2024].
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