Itineraries of rigid rotations and diffeomorphisms of the circle

作者：Richeson David; Winkler Paul; Wiseman Jim^*

来源：Theoretical Computer Science, 2010, 411(1): 259-265.

DOI：10.1016/j.tcs.2009.09.034

• Symbolic dynamics
• Rotations

We examine the itinerary of 0 is an element of S(1) = R/Z under the rotation by alpha is an element of R\Q. The motivating question is: if we are given only the itinerary of 0 relative to I subset of S(1), a finite union of closed intervals, can we recover alpha and I? We prove that the itineraries do determine alpha and I up to certain equivalences. Then we present elementary methods for Finding alpha and I. Moreover, if g : S(1) -> S(1) is a C(2), orientation preserving diffeomorphism with an irrational rotation number, then we can use the orbit itinerary to recover the rotation number up to certain equivalences.

• 出版日期2010-1-1