Basins of attraction in Loewner equations
Complex Variables
2012-02-20 v2 Dynamical Systems
Abstract
We prove that any Loewner PDE whose driving term h(z,t) vanishes at the origin, and satisfies the bunching condition r m(Dh(0,t))\geq k(Dh(0,t)) for some r\in R^+, admits a solution given by univalent mappings (f_t: B^q\to C^q). This is done by discretizing time and considering the abstract basin of attraction. If r<2, then the union of the images f_t(\B^q) of a such solution is biholomorphic to C^q.
Keywords
Cite
@article{arxiv.1108.6000,
title = {Basins of attraction in Loewner equations},
author = {Leandro Arosio},
journal= {arXiv preprint arXiv:1108.6000},
year = {2012}
}
Comments
9 pages, revised exposition, improved results, added references