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2018 Complex rotation numbers: bubbles and their intersections
Nataliya Goncharuk
Anal. PDE 11(7): 1787-1801 (2018). 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.

Citation

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Nataliya Goncharuk. "Complex rotation numbers: bubbles and their intersections." Anal. PDE 11 (7) 1787 - 1801, 2018. https://doi.org/10.2140/apde.2018.11.1787

Information

Received: 3 August 2017; Revised: 8 December 2017; Accepted: 9 April 2018; Published: 2018
First available in Project Euclid: 15 January 2019

zbMATH: 1388.37049
MathSciNet: MR3810472
Digital Object Identifier: 10.2140/apde.2018.11.1787

Subjects:
Primary: 37E10, 37E45

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 7 • 2018
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