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
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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.


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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
Received by editor(s): December 29, 1994
Communicated by: Linda Keen
Article copyright: © Copyright 1996 American Mathematical Society