Student author: Paul Winkler
Theoretical Computer Science
We examine the itinerary of 0 ∈ S1 = R/Z under the rotation by α ∈ R \ Q. The motivating question is: if we are given only the itinerary of 0 relative to I ⊂ S1 , a finite union of closed intervals, can we recover α and I? We prove that the itineraries do determine α and I up to certain equivalences. Then we present elementary methods for finding α and I. Moreover, if g : S1 → S1 is a C2 , orientation preserving diffeomorphism with an irrational rotation number, then we can use the orbit itinerary to recover the rotation number up to certain equivalences.
Richeson, David S.; Winkler, Paul; and Wiseman, Jim, "Itineraries of Rigid Rotations and Diffeomorphisms of the Circle" (2010). Dickinson College Faculty Publications. Paper 1395.