# A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives

## TL;DR

This paper proves that commuting circle diffeomorphisms with certain smoothness conditions and independent rotation numbers are simultaneously conjugate to rotations, extending Denjoy's theorem to a broader class of maps.

## Contribution

It establishes a new Denjoy-type result for multiple commuting circle diffeomorphisms with mixed Hölder derivatives and specific smoothness sum conditions.

## Key findings

- Maps are conjugate to rotations under given conditions
- Rotation numbers must be independent over rationals
- Smoothness sum exceeds one

## Abstract

We prove that if d is an integer number bigger than 1 and f_1,...,f_d are commuting circle diffeomorphisms respectively of class C^(1+\tau_k), where \tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate to rotations provided that their rotation numbers are independent over the rationals.