Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem — connecting symmetries with constants of the motion — within a reduction. This is the first of two papers, and it focuses on the reduction within the Poisson and the symplectic formalism.

中文翻译：

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对称性和约简第一部分——泊松和辛图

与狄拉克提出的类比原则相一致，我们描述了减少经典动力学的一般设置，以及诺特定理（将对称性与运动常数联系起来）在减少中的作用。这是两篇论文中的第一篇，它侧重于泊松内的约简和辛形式主义。