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.

中文翻译：

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平面多项式哈密顿系统的线性化

重新审视了二维多项式哈密顿系统的等时性和线性化，并提出了新的结果。我们给出了一个新的计算程序来获得多项式系统线性化的充分必要条件。使用计算机代数系统，我们为具有 5、6 和 7 次齐次非线性的哈密顿系统的线性化提供了充分必要条件。我们还为具有 2、3 和 5 次非齐次非线性的系统提供了一些充分条件。