Bifurcations of periodic solutions of Hamiltonian systems using fixed point methods
In this article the author studies the bifurcations of periodic solutions of periodic Hamiltonian systems on \(\mathbb{R}^4\) with two degrees of freedom depending on two parameters, say, \(\mu\) and \(\nu\). By analysing the 4-jet of the normal forms of the Hamiltonian systems, the author is able to find a region \(S\) in the \(\mu,\nu\)-parameter plane bounded by two smooth curves where bifurcations occur. It is proved that on the curves the system has at least two periodic solutions while in the region \(S\) there are at least three periodic solutions.
scientific article; zbMATH DE number 1014352