Versal normal form for nonsemisimple singularities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Mokhtari, Fahimeh¹  Sanders, Jan A.¹ 

[1] Vrije Univ, Fac Sci, Dept Math, De Boelelaan 1081a, NL-1081 HV Amsterdam, Netherlands

关键词: Versal normal form;    L-4 problem;    Nilpotent;    sl(2) representation;   

DOI  :  10.1016/j.jde.2019.03.039

来源: Elsevier

【 摘 要 】

The theory of versal normal form has been playing a role in normal form since the introduction of the concept by V.I. Arnol'd in [1,2]. But there has been no systematic use of it that is in line with the semidirect character of the group of formal transformations on formal vector fields, that is, the linear part should be done completely first, before one computes the nonlinear terms. In this paper, we address this issue by giving a complete description of a first order calculation in the case of the two- and three-dimensional irreducible nilpotent cases, which is then followed up by an explicit almost symplectic calculation to find the transformation to versal normal form in a particular fluid dynamics problem and in the celestial mechanics L-4 problem. (C) 2019 The Authors. Published by Elsevier Inc.

【 授权许可】

Free