Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

One-way intervals of circle maps


Authors: Lauren W. Ancel and Michael W. Hero
Journal: Proc. Amer. Math. Soc. 126 (1998), 1191-1197
MSC (1991): Primary 54H20, 34C35, 58F03
MathSciNet review: 1476114
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An interval in the circle $S^1$ is one-way with respect to a map $f:S^1\to S^1$ if under repeated applications of $f$ all points of the interval move in the same direction. The main result is that every locally one-way interval is either one-way or is the union of two overlapping one-way subintervals. An example is given which illustrates that the latter case can occur; however, it is proved that the latter case cannot occur if the interval is covered by the image of the map. As a corollary, it is shown that if $f$ has periodic points, then every interval which contains no periodic points is either one-way or is the union of two overlapping one-way subintervals.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54H20, 34C35, 58F03

Retrieve articles in all journals with MSC (1991): 54H20, 34C35, 58F03


Additional Information

Lauren W. Ancel
Affiliation: Department of Biological Sciences, Stanford University, Stanford, California 94305
Email: ancel@charles.stanford.edu

Michael W. Hero
Affiliation: Equable Securities Corporation, 300 N. 121 Street, Milwaukee, Wisconsin 53226

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04652-8
PII: S 0002-9939(98)04652-8
Received by editor(s): January 31, 1995
Received by editor(s) in revised form: January 10, 1996
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society