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SEMINARS
Symmetries of Ordinary Differential Equations (I)
时间  Datetime
2019-09-12 14:30 — 16:00 
地点  Venue
Large Conference Room(706)
报告人  Speaker
Sebastian Walcher
单位  Affiliation
Mathematik A - RWTH Aachen
邀请人  Host
张祥
报告摘要  Abstract

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, requiring only minimal prerequisites. Their purpose is mostly to provide a quick approach for nonspecialists; they are certainly not intended to replace any of the monographs on this topic. There is a certain emphasis on ODEs of first order here, which are less prominently featured in most standard texts. The notes are organized as follows. Chapter 1 contains basic and introductory material on ODEs with analytic right hand side, much of which is probably known to the reader. (Some remarks address differential equations with smooth right hand side, pointing out similarities and differences.) Chapter 2 contains Sophus Lie’s classical theory of local one-parameter symmetry and orbital symmetry groups in the context of first order (mostly autonomous) equations, with a short digression to second order equations. Chapter 3 deals with “multiparameter symmetries” (including a clarification notions), and with invariant sets that are (so to speak) forced by symmetries. In Chapter 4 the table is turned: We start with a given (linear) group and discuss differential equations that admit this group as a group of symmetries, with an emphasis on toral groups. We then discuss Poincar´e-Dulac normal forms as a special class admitting toral symmetry groups.