Uniformizing complex ODEs and applications

Details Uniformizing complex ODEs and applications Uniformizing complex ODEs and applications

2011-11-09

arxiv.org/abs/1111.2365v1

Mathematics

Dynamical Systems

Scientific paper

We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some well-known phenomena related to the presence of metrics with positive curvature. Several applications of these ideas are provided including a type of "confinement theorem" for solutions of complete polynomial vector fields on $\mathbb{C}^n$ and obstructions for certain (germs of) vector fields to be realized by a global holomorphic vector field on a compact K\"ahler manifold. As a complement a new approach to certain classical equations is proposed and detailed in the case of Halphen equations.

Affiliated with

Also associated with

No associations

Rating

Uniformizing complex ODEs and applications 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 Uniformizing complex ODEs and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniformizing complex ODEs and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727622