报告主题： 超可积系统
报告人：Allan Fordy 教授 （英国 University of Leeds）
报告时间：2019年4月3日（周三）14：30
报告地点：校本部乐乎楼 大学厅
邀请人：张大军
主办部门：太阳成集团tyc33455数学系
报告摘要：This talk starts with an expository description of what superintegrability is and how it differs from complete integrability. Using the system of two harmonic oscillators we see that in the non-resonant case we have only 2 first integrals, with quasi-periodic motion. The resonant case is superintegrable and the additional integrals give us periodic motion, with Lissajous figures being described by algebraic curves, being the level sets of the first integrals. In the quantum case this leads to degeneracy of the eigenvalues, with commuting operators laddering us between the eigenfunctions.
The main part of the talk will be about the classical case and concentrate on how to build superintegrable systems with kinetic energies defined on various geometric spaces.
In the constant curvature case, we have an abundance of isometries, giving us a systematic way of constructing first integrals. This quickly leads to separable systems, which can then be restricted, by the addition of further integrals, to yield superintegrable ones. We discuss the resulting non-commutative Poisson algebras.
After constant curvature, we consider conformally flat spaces, which no longer have so many isometries, but do have conformal symmetries. We give a method of using the latter to build first integrals, leading to Darboux-Koenigs systems and some 3D generalisations.
Finally, we consider the notion of Kaluza-Klein Reduction, allowing us to reduce a 3D superintegrable system to a 2D one, with the latter inheriting its superintegrability from the 3D one.
欢迎教师、员工参加！
