Nilpotent normal form for divergence-free vector fields and volume-preserving maps

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Dullin, H. R.¹  Meiss, J. D.¹ 

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

关键词: nilpotent normal form;    divergence-free vector fields;    volume-preserving maps;   

DOI  :  10.1016/j.physd.2007.08.014

来源: Elsevier

【 摘 要 】

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence-free vector field in R-3 has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial with the same degree. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free