Proper trajectories of type C* of a polynomial vector field on C2
Complex Variables
2010-10-29 v1 Classical Analysis and ODEs
Dynamical Systems
Abstract
We prove that if a polynomial vector field on C2 has a proper and non-algebraic trajectory analytically isomorphic to C* all its trajectories are proper, and except at most one which is contained in an algebraic curve of type C all of them are of type C*. As corollary we obtain an analytic version of Lin-Zaidenberg Theorem for polynomial foliations.
Keywords
Cite
@article{arxiv.1010.6055,
title = {Proper trajectories of type C* of a polynomial vector field on C2},
author = {Alvaro Bustinduy},
journal= {arXiv preprint arXiv:1010.6055},
year = {2010}
}
Comments
To appear in Mathematische Annalen