Symplectic transformations and periodic solutions of Hamiltonian systems
The paper deals with the existence of periodic solutions of Hamiltonian systems, both for the first-order Hamiltonian systems \[ \dot x=Hy(t,x,y),\quad \dot y=-H_x(t,x,y)\tag{1} \] and the second-order Hamiltonian systems \[ -\ddot y=V_y(t,y).\tag{2} \] Note that equation (2) is a special case of (1) with \(H=\frac 12|x|^2+V(t,y)\). The aim of this paper is to understand the relationship between (1) and (2). The author shows that a superquadratic (subquadratic) (2) is equivalent to superquadratic (subquadratic) (1) by a symplectic transformation.
scientific article; zbMATH DE number 1218641