Rotation domains for maps of bounded type
Dynamical Systems
2026-05-21 v1
Abstract
We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and several complex variables, starting with a version of the classical theorem of Arnol'd and ending with a result on persistence of Herman rings in families of two-dimensional maps.
Cite
@article{arxiv.2605.20376,
title = {Rotation domains for maps of bounded type},
author = {Nataliya Goncharuk and Michael Yampolsky},
journal= {arXiv preprint arXiv:2605.20376},
year = {2026}
}