Boundaries of rotation sets for homeomorphisms of the 𝑛-torus

Swanson, Richard; Walker, Russell

doi:10.1090/S0002-9939-96-03426-0

Boundaries of rotation sets for homeomorphisms of the $n$-torus
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by Richard Swanson and Russell Walker PDF

Proc. Amer. Math. Soc. 124 (1996), 3247-3255 Request permission

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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