A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e. g., a boundary, an obstacle or a set of admissible states). In this paper we give local classification results for all typical singularities of sections of regular (non-singular) Hamiltonian systems, a problem equivalent to the classification of typical singularities of Hamiltonian systems with one-sided constraints. In particular, we give a complete list of exact normal forms with functional invariants, and we show how these are related/obtained by the symplectic classification of mappings with prescribed (Whitney-type) singularities, naturally defined on the reduced phase space of the Hamiltonian system.

哈密​​顿系统的一部分是系统相空间中的超曲面，通常表示一组单边约束（例如，边界、障碍物或一组可容许状态）。在本文中，我们给出了正则（非奇异）哈密顿系统截面的所有典型奇点的局部分类结果，该问题等效于具有单边约束的哈密顿系统典型奇点的分类。特别是，我们给出了具有函数不变量的精确正规形式的完整列表，并且我们展示了这些是如何通过具有指定（惠特尼型）奇点的映射的辛分类来相关/获得的，自然地定义在哈密顿量的缩减相空间上系统。