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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Boundaries of rotation sets
for homeomorphisms of the $n$-torus


Authors: Richard Swanson and Russell Walker
Journal: Proc. Amer. Math. Soc. 124 (1996), 3247-3255
MSC (1991): Primary 58J22
MathSciNet review: 1328381
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Abstract: We construct a $C^\omega $ diffeomorphism of the 3-torus whose rotation set is not closed. We prove that the rotation set of a homeomorphism of the $n$-torus contains the extreme points of its closed convex hull. Finally, we show that each pseudo-rotation set is closed for torus homeomorphisms.


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Additional Information

Richard Swanson
Affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717-0240
Email: dswanson@math.montana.edu

Russell Walker
Affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717-0240
Email: walker@math.montana.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03426-0
Keywords: Rotation vectors on tori
Received by editor(s): April 4, 1995
Additional Notes: Research supported in part by NSF-OSR grant #9350546
Communicated by: Linda Keen
Article copyright: © Copyright 1996 American Mathematical Society