Consecutive shifts along orbits of vector fields

Details Consecutive shifts along orbits of vector fields Consecutive shifts along orbits of vector fields

2005-10-28

arxiv.org/abs/math/0510625v1

Mathematics

Differential Geometry

9 pages, submitted to the Proceedings of the conference FOLIATIONS-2005, Poland, Lodz

Scientific paper

Let $M$ be a smooth ($C^{\infty}$) manifold, $F_1,...,F_n$ be vector fields on $M$ generating the corresponding flows $\Phi_1,...,\Phi_n$, and $\alpha_1,...,\alpha_{n}:M\to \mathbb{R}$ smooth functions. Define the following map $f:M\to M$ by $$f(x)= \Phi_n (... (\Phi_2 (\Phi_1 (x,\alpha_1(x)), \alpha_2(x)), ..., \alpha_n(x)).$$ In this note we give a necessary and sufficient condition on vector fields $F_1,...,F_n$ and smooth functions $\alpha_1,...,\alpha_{n}$ for $f$ to be a local diffeomorphism. It turns out that this condition is invariant with respect to the simultaneous permutation of the corresponding vector fields and functions.

Affiliated with

Also associated with

No associations

Rating

Consecutive shifts along orbits of vector fields 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 Consecutive shifts along orbits of vector fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Consecutive shifts along orbits of vector fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-500621