Period function for a class of Hamiltonian systems

[摘要] This paper studies the period function of the class of Hamiltonian systems (x)overdot = - H-y, y(overdot) = H-x, where H(x, y) has the special form H(x, y) = F(x) + G(y) and the origin is a non-degenerate center. More concretely, if T(h) denotes the period of the periodic orbit contained in H(x, y) = h we solve the inverse problem of chatacterizing all systems with a given function T(h). We also characterize the limiting behaviour of T at infinity when the origin is a global center and apply this result to prove, among other results, that there are no nonlinear polynomial isochronous centers in this family. (C) 2000 Academic Press.

[发布日期] 2000-11-20

[关键词] Hamiltonian system;inverse problem;period function;isochronicity