© 2015 Elsevier Inc. 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 : 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.
- Hamiltonian systems
- Isochronous centers