Semigroups versus evolution families in the Loewner theory
Complex Variables
2009-07-27 v1 Dynamical Systems
Abstract
We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated variables. This is the case if and only if the evolution family comes from a semigroup of holomorphic self-maps of the disc.
Cite
@article{arxiv.0907.4324,
title = {Semigroups versus evolution families in the Loewner theory},
author = {Filippo Bracci and Manuel D. Contreras and Santiago Diaz-Madrigal},
journal= {arXiv preprint arXiv:0907.4324},
year = {2009}
}
Comments
19 pages