  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.
