Denjoy's_theorem_on_rotation_number
Denjoy's theorem on rotation number
When a diffeomorphism of the circle is topologically conjugate to an irrational rotation
In mathematics, the Denjoy theorem gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational rotation. Denjoy (1932) proved the theorem in the course of his topological classification of homeomorphisms of the circle. He also gave an example of a C1 diffeomorphism with an irrational rotation number that is not conjugate to a rotation.