Nataliya Goncharuk
Published 2017-08-03Version 1
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.
A circle diffeomorphism with breaks that is smoothly linearizable
Self-similarity of bubbles
Dimensional characteristics of invariant measures for circle diffeomorphisms
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