Periodic orbits of a one dimensional non autonomous Hamiltonian system
Classical Analysis and ODEs
2010-12-30 v1 Mathematical Physics
math.MP
Abstract
In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite number of periodic solutions with a given {\rho}. We give a lower bound on the number of periodic orbits with a given period and {\rho} by means of the Morse theory.
Cite
@article{arxiv.1012.5613,
title = {Periodic orbits of a one dimensional non autonomous Hamiltonian system},
author = {Jacopo Bellazzini and Vieri Benci and Marco G. Ghimenti},
journal= {arXiv preprint arXiv:1012.5613},
year = {2010}
}