论文标题
汉密尔顿系统的部分
Sections of Hamiltonian Systems
论文作者
论文摘要
哈密顿系统的一部分是系统相位空间中的一个hyperface，通常代表一组单方面的约束（例如边界，障碍物或一组可接受的状态）。在本文中，我们为常规（非单明）哈密顿系统的所有典型奇异性提供了局部分类结果，这是一个与单方面约束的哈密顿系统典型奇异性分类的问题。特别是，我们提供了具有功能不变的确切正常形式的完整列表，我们展示了如何通过使用规定的（惠特尼（Whitney-type））奇异性对映射进行映射的相关性分类，自然定义在汉密尔顿系统的减少相空间上。
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.
