Complex rotation numbers: bubbles and their intersections
Dynamical Systems
2018-06-06 v1
Abstract
The construction of complex rotation numbers, due to V.Arnold, gives rise to a fractal-like set "bubbles" related to a circle diffeomorphism. "Bubbles" is a complex analogue to Arnold tongues. This article contains a survey of the known properties of bubbles, as well as a variety of open questions. In particular, we show that bubbles can intersect and self-intersect, and provide approximate pictures of bubbles for perturbations of M\"obius circle diffeomorphisms.
Cite
@article{arxiv.1708.01077,
title = {Complex rotation numbers: bubbles and their intersections},
author = {Nataliya Goncharuk},
journal= {arXiv preprint arXiv:1708.01077},
year = {2018}
}