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

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

2007-06-11

arxiv.org/abs/0706.1575v1

Nonlinear Sciences

Chaotic Dynamics

laTeX, 20 pages, 1 figure

Scientific paper

10.1016/j.physd.2007.08.014

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 $\mathbb{R}^3$ 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 inverse with the same degree.

Affiliated with

Also associated with

No associations

Rating

Nilpotent normal form for divergence-free vector fields and volume-preserving maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nilpotent normal form for divergence-free vector fields and volume-preserving maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nilpotent normal form for divergence-free vector fields and volume-preserving maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-358729