报告题目 (Title)：Deautonomisation of integrable mappings and degree growth：I, II, III （可积系统的非自治化与熵增长）
报告人 (Speaker)：Alexander Stokes 博士（早稻田大学，日本）
报告时间 (Time)：(I): 2024年9月20日 15:40-17:10
(II): 2024年9月21日 14:00-15:30
(III): 2024年9月21日 15:40-17:10
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：张大军
主办部门：永利数学系
报告摘要：
In discrete integrable systems, the idea of taking an integrable birational mapping of the plane and cooking up a ‘non-autonomous version’ of it with integrability properties preserved is best known as a path from QRT maps to discrete Painlevé equations. This is often done using singularity confinement, which can be formulated in terms of the geometry of rational surfaces. The aim of these talks is to give a pedagogical introduction to several topics under the theme of deautonomisation, beginning with how to perform deautonomisation by singularity confinement of a mapping of the plane on the level of geometry. We will then discuss the relation between parameter evolution and degree growth when deautonomisation by singularity confinement is performed on non-integrable mappings. Time permitting, we will also introduce a novel example of elliptic nature with links to algebraic dynamics and some examples beyond dimension two.
