Linearizability of planar polynomial Hamiltonian systems

Abstract

Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system. Using computer algebra systems we provide necessary and sufficient conditions for linearizability of Hamiltonian systems with homogeneous non-linearities of degrees 5, 6 and 7. We also present some sufficient conditions for systems with nonhomogeneous nonlinearities of degrees two, three and five.

We thank the referees for the careful reading and valuable suggestions which helped to improve the manuscript. The first and third authors are supported by the Slovenian Research Agency (core research program P1-0306). The second author is partially supported by a MINECO/FEDER grant number PID2020-113758GB-I00 and an AGAUR, Spain (Generalitat de Catalunya) grant number 2017SGR-1276.