Vol. 11, No. 7, 2018
Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Complex rotation numbers: bubbles and their intersections

Nataliya Goncharuk
Vol. 11 (2018), No. 7, 1787–1801
DOI: 10.2140/apde.2018.11.1787
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 Möbius circle diffeomorphisms.

Keywords
complex tori, rotation numbers, diffeomorphisms of the circle
Mathematical Subject Classification 2010
Primary: 37E10, 37E45
Milestones
Received: 3 August 2017
Revised: 8 December 2017
Accepted: 9 April 2018
Published: 20 May 2018
Authors
Nataliya Goncharuk
Department of Mathematics
Cornell University
Ithaca, NY
United States