A class of isochronous polynomial Hamiltonians (Q2764790)

The paper deals with an isochronous Hamiltonian of the plane \(\mathbb{R}^2\). Indeed, let \(H_0= \frac{x^2+y^2}{2}+\) higher order terms be an isochronous Hamiltonian, then the author presents a necessary condition for a system to be isochronous. This result can be considered as a generalization of the isochronous behaviour of the Hamiltonian \(H_0= \frac{x^2+y^2}{2}+\) homogeneous polynomial of previous results [see \textit{C. J. Christopher} and \textit{J. Devlin}, SIAM J. Math. Anal. 28, 162-177 (1997; Zbl 0881.34057)].