A complete geometric classification of symmetries of autonomous Hamiltonian systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.

中文翻译：

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哈密​​顿自治系统的对称性和守恒量的总结

建立了自治哈密顿系统对称性的完整几何分类；说明在所有情况下如何获取其相关的保守量。特别是，首先，我们回顾一下关于哈密顿量和辛形式的对称性的著名结果和性质，然后介绍和研究一些新型的非辛对称性及其守恒量。