Self-similarity of bubbles

TL;DR

This paper investigates the fractal structure of bubbles related to circle diffeomorphisms, demonstrating an approximate self-similarity property that enhances understanding of their complex geometric nature.

Contribution

It introduces the concept of approximate self-similarity in bubbles, providing new insights into their fractal structure and relation to Arnold tongues.

Findings

Bubbles exhibit approximate self-similarity.

The study links bubbles to complex fractal geometries.

Results deepen understanding of circle diffeomorphism dynamics.

Abstract

Bubbles is a fractal-like set related to a circle diffeomorphism; they are a complex analogue to Arnold tongues. In this article, we prove an approximate self-similarity of bubbles.