Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat

2016/05/25 by Cresson, Jacky, Palafox, Jordy
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.07775

Abstract

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.

Related

• Trivial Isochronous Centers in Odd Degrees: a Two--Branch Picture
• Topological properties on isochronous centers of polynomial Hamiltonian differential systems
• Isochronicity conditions for some planar polynomial systems
• Isochronicity conditions for some real polynomial systems
• About a conjecture for uniformly isochronous polynomial centers