Isochronous centers of polynomial Hamiltonian systems and a conjecture   of Jarque and Villadelprat
  We study the conjecture of Jarque and Villadelprat stating that every center of a planar polynomial Hamiltonian system of even degree is nonisochronous. This conjecture is proved for quadratic and quartic systems. Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large. 
Jacky Cresson and Jordy Palafox
math.DS