Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Richard Swanson; 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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