Bolsinov Alexey, Guglielmi Lorenzo, Kudryavtseva Elena
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia.
Philos Trans A Math Phys Eng Sci. 2018 Sep 17;376(2131):20170424. doi: 10.1098/rsta.2017.0424.
We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.
我们讨论了具有两个自由度的可积哈密顿系统中抛物轨道和尖点环面的范式和辛不变量。此类奇点出现在几何和数学物理中的许多可积系统中，可被视为退化奇点的最简单示例。我们还提出了一些新技术，显然可用于研究更一般类型的退化奇点的辛不变量。本文是主题为“有限维可积系统：新趋势和方法”的一部分。
