Roles

Student author: Paul Winkler

Document Type

Article

Publication Date

1-2010

Department

Mathematics

Language

English

Publication Title

Theoretical Computer Science

Abstract

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 IS1 , 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 : S1S1 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.

Comments

Published as:
Richeson, David, Paul Winkler, and Jim Wiseman. "Itineraries of Rigid Rotations and Diffeomorphisms of the Circle." Theoretical Computer Science 411, no. 1 (2010): 259-265. https://www.sciencedirect.com/science/article/pii/S030439750900704X

© 2009 Elsevier B.V. All rights reserved.

This author post-print is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Science Direct's Website.

© 2010. This publication is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/

DOI

10.1016/j.tcs.2009.09.034

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