Isochronicity and linearizability of planar polynomial Hamiltonian systems

Abstract

Agraïments: UNAB13-4E-1604. The second author is supported by the Slovenian Research Agency. Both authors are supported by the grant FP7-PEOPLE-2012-IRSES-316338. We also thank the referee for valuable remarks which helped to improve the manuscript.

In this paper we study isochronicity and linearizability of planar polynomial Hamiltonian systems. First we prove a theorem which supports a negative answer to the following open question stated by Jarque and Villadelprat in [15]: Do there exist planar polynomial Hamiltonian systems of even degree having an isochronous center? Additionally we obtain some conditions for linearizability of complex cubic Hamiltonian systems.