论文标题
综合哈密顿系统的单轨道理论的最新进展
Recent advances in the monodromy theory of integrable Hamiltonian systems
论文作者
论文摘要
J. J. Duistermaat引入了单肌的概念，是对全球动作坐标在可综合的哈密顿系统中存在的首次障碍。此后对这种不变的研究进行了广泛的研究，并被证明是在有限维置系统的各种具体示例中并非普通的。本文的目的是简要概述单片，并讨论其一些概括。特别是，我们将讨论围绕聚焦的奇异性以及量子，分数和散射单片的概念。博览会将与许多例子和开放问题相辅相成。
The notion of monodromy was introduced by J. J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be non-trivial in various concrete examples of finite-dimensional integrable systems. The goal of the present paper is to give a brief overview of monodromy and discuss some of its generalisations. In particular, we will discuss the monodromy around a focus-focus singularity and the notions of quantum, fractional and scattering monodromy. The exposition will be complemented with a number of examples and open problems.
