Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem
Keywords
Periodic solutions, Poincaré-Birkhoff, nonlinear dynamicsAbstract
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.Downloads
Published
2012-04-23
How to Cite
1.
FONDA, Alessandro, SABATINI, Marco and 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 April 2012. Vol. 40, no. 1, pp. 29 - 52. [Accessed 20 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0