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Complex rotation
numbers: bubbles and their intersections
Nataliya Goncharuk |
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Vol. 11 (2018), No. 7, 1787–1801
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 37E10, 37E45
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Milestones
Received: 3 August 2017
Revised: 8 December 2017
Accepted: 9 April 2018
Published: 20 May 2018
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Authors |
| Nataliya Goncharuk | |
| Department of Mathematics Cornell University Ithaca, NY United States |
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