Reparametrizations of vector fields and their shift maps

Details Reparametrizations of vector fields and their shift maps Reparametrizations of vector fields and their shift maps

2009-07-02

arxiv.org/abs/0907.0354v1

Mathematics

Dynamical Systems

To appear in the Proceeding of Institute of Mathematics of NAS of Ukraine. 7 pages, no figures

Scientific paper

Let M be a smooth manifold, F be a smooth vector field on M, and F_t be the local flow of F. Denote by Sh(F) the space of smooth maps h:M-->M of the following form: h(x) = F_{f(x)}(x), where f:M-->R runs over all smooth functions on M which can be substituted into the flow F_t instead of time. This space often coincides with the identity component of the group of diffeomorphisms preserving orbits of F. In this note it is shown that Sh(F) is not changed under reparametrizations and pushforwards of F. As an application it is proved that a vector field F without non-closed orbits can be reparametrized to induce a circle action on M if and only if there exists a smooth function f:M-->(0,+\infty) such that for each non-singular point x of M, the value f(x) is an integer multiple of the period of x with respect to F.

Affiliated with

Also associated with

No associations

Rating

Reparametrizations of vector fields and their shift 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 Reparametrizations of vector fields and their shift maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reparametrizations of vector fields and their shift maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-730757