# Nilpotent normal form for divergence-free vector fields and volume-preserving maps - Nonlinear Sciences > Chaotic Dynamics

Nilpotent normal form for divergence-free vector fields and volume-preserving maps - Nonlinear Sciences > Chaotic Dynamics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We study the normal forms for incompressible flows and maps in theneighborhood of an equilibrium or fixed point with a triple eigenvalue. Weprove that when a divergence free vector field in \$\mathbb{R}^3\$ has nilpotentlinearization with maximal Jordan block then, to arbitrary degree, coordinatescan be chosen so that the nonlinear terms occur as a single function of twovariables in the third component. The analogue for volume-preservingdiffeomorphisms gives an optimal normal form in which the truncation of thenormal form at any degree gives an exactly volume-preserving map whose inverseis also polynomial inverse with the same degree.

Autor: H.R. Dullin, J.D. Meiss

Fuente: https://arxiv.org/