Minimal C^1 diffeomorphisms of the circle which admit measurable fundamental domains

TL;DR

This paper constructs minimal C^1-diffeomorphisms of the circle with any irrational rotation number that possess measurable fundamental domains, advancing understanding of circle dynamics and measurable structures.

Contribution

It introduces a method to explicitly construct minimal C^1-diffeomorphisms with prescribed irrational rotation numbers that admit measurable fundamental domains.

Findings

Existence of minimal C^1-diffeomorphisms with measurable fundamental domains for all irrational rotation numbers.

Explicit construction techniques for such diffeomorphisms.

Insights into the relationship between smoothness, minimality, and measure-theoretic properties.

Abstract

We construct, for each irrational number $\alpha$, a minimal $C^1$-diffeomorphism of the circle with rotation number $\alpha$ which admits a measur