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)

 

Forcing of periodic orbits for interval maps
and renormalization of piecewise affine maps


Authors: Marco Martens and Charles Tresser
Journal: Proc. Amer. Math. Soc. 124 (1996), 2863-2870
MSC (1991): Primary 58F11
MathSciNet review: 1343712
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for continuous maps on the interval, the existence of an $n$-cycle implies the existence of $n-1$ points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise affine maps (with no zero slope) cannot be infinitely renormalizable.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F11

Retrieve articles in all journals with MSC (1991): 58F11


Additional Information

Marco Martens
Affiliation: Institute of Mathematical Sciences, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: marco@math.sunysb.edu

Charles Tresser
Affiliation: I.B.M., P.O. Box 218, Yorktown Heights, New York 10598
Email: tresser@watson.ibm.com

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03508-3
PII: S 0002-9939(96)03508-3
Received by editor(s): December 29, 1994
Communicated by: Linda Keen
Article copyright: © Copyright 1996 American Mathematical Society