沿Seifert流形的平行输运与分式单值性
Parallel transport along Seifert manifolds and fractional monodromy
摘要：
分数单值性的概念是由Nekhoroshev、Sadovskií和Zhilinskií引入的，作为Duistermaat从环面丛到奇异环面纤维化的意义上的标准（“整数”）单值性的推广。在本文中，我们证明了一个一般的结果，允许计算分数monodromy在各种可积的哈密顿系统。特别是，我们表明，非平凡的分数monodromy在2度自由度系统的Hamilton圈行动只涉及到不动点的圈行动。我们的方法是基于一个特定的概念，沿着塞弗特流形的平行运输的研究。
英文摘要：
The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (`integer') monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.
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