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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

A priori degeneracy of one-dimensional rotation sets for periodic point free torus maps


Author: Jaroslaw Kwapisz
Journal: Trans. Amer. Math. Soc. 354 (2002), 2865-2895
MSC (1991): Primary 37E45, 37E30
Published electronically: March 7, 2002
MathSciNet review: 1895207
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Abstract: Diffeomorphisms of the two torus that are isotopic to the identity have rotation sets that are convex compact subsets of the plane. We show that certain line segments (including all rationally sloped segments with no rational points) cannot be realized as a rotation set.


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Additional Information

Jaroslaw Kwapisz
Affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717-2400
Email: jarek@math.montana.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02952-5
PII: S 0002-9947(02)02952-5
Received by editor(s): January 10, 2001
Received by editor(s) in revised form: August 31, 2001
Published electronically: March 7, 2002
Additional Notes: Partially supported by NSF grant DMS-9970725 and MONTS-190729.
Article copyright: © Copyright 2002 Jaroslaw Kwapisz