Motivated by the theory of Painlevé equations and associated hierarchies, we study nonautonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed into a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-Stäckel systems from [14].

中文翻译：

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变形李代数与Frobenius可积非自治哈密顿系统。

受Painlevé方程和相关层级理论的推动，我们研究了Frobenius可积的非自治哈密顿系统。我们建立了充分的条件，在此条件下，哈密​​顿向量场的给定有限维李代数可以变形为与原始代数相同分布的Frobenius可积向量场的时变李代数。将结果应用于[ 14]中的准Stäckel系统。