This website requires JavaScript.

Hamiltonian structure of rational isomonodromic deformation systems

M. BertolaJ. HarnadJ. Hurtubise
Dec 2022
摘要
The Hamiltonian approach to isomonodromic deformation systems is extended toinclude generic rational covariant derivative operators on the Riemann spherewith irregular singularities of arbitrary Poincar\'e rank. The space ofrational connections with given pole degrees carries a natural Poissonstructure corresponding to the standard classical rational R-matrix structureon the dual space $L^*{\mathfrak g}(r)$ of the loop algebra $L{\mathfrakg}(r)$. Nonautonomous isomonodromic counterparts of the isospectral systemsgenerated by spectral invariants are obtained by identifying the deformationparameters as Casimir invariants on the phase space. These are shown tocoincide with the higher {\it Birkhoff invariants} determining the localasymptotics near to irregular singular points, together with the pole loci. Infinitesimal isomonodromic deformations are shown to be generated by the sumof the Hamiltonian vector field and an {\em explicit derivative} vector fieldthat is transversal to the symplectic foliation. The Casimir invariants serveas coordinates complementing those along the symplecticeaves, extended by the{\it exponents of formal monodromy}, defining a local symplectomorphism betweenthem. The explicit derivative vector fields preserve the Poisson structure anddefine a flat {\it transversal connection}, spanning an integrable distributionwhose leaves, locally, may be identified as the orbits of a free abelian group.The projection of the infinitesimal isomonodromic deformations vector fields tothe quotient manifold under this action gives the commuting Hamiltonian vectorfields corresponding to the spectral invariants dual to the Birkhoff invariantsand the pole loci.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答