Itineraries of rigid rotations and diffeomorphisms of the circle

David Richeson, Paul Winkler, Jim Wiseman

We examine the itinerary of $0\in S^1=\mathbb{R}/\mathbb{Z}$ under the rotation by $α\in\R\bs\Q$. The motivating question is: if we are given only the itinerary of 0 relative to $I\subset S^1$…