汇报标题 (Title)：Deautonomisation of integrable mappings and degree growth：I, II, III （可积系统的非自治化与熵增长）
汇报人 (Speaker)：Alexander Stokes 博士（早稻田大学，日本）
汇报功夫 (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
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：张雄师
主办部门：理学院数学系
汇报提要：
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.
