从Gauss-Manin单值性导出分数Hamilton单值性
Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy
摘要：
分数Hamilton Monodromy是最近由N. N. Nekhoroshev，D. A. Sadovskii和B. I. Zhilinskii的能量动量映射，其图像具有一种特殊类型的非孤立奇点。在本文中，我们分析了分数Hamilton Monodromy的概念的高斯-Manin Monodromy的黎曼曲面构造的能量-动量映射和相关的一个循环在复杂的空间中，绕过奇点线。我们还证明了1：-n和m：-n共振系统的分数阶Hamilton Monodromy的一些命题。
英文摘要：
Fractional Hamiltonian Monodromy is a generalization of the notion of Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A. Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a particular type of non-isolated singularities. In this paper, we analyze the notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin Monodromy of a Riemann surface constructed from the energy-momentum map and associated to a loop in complex space which bypasses the line of singularities. We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n and m:-n resonant systems.
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