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Proceedings of the American Mathematical Society

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

 

 

Rotation sets of toral flows


Authors: John Franks and Michał Misiurewicz
Journal: Proc. Amer. Math. Soc. 109 (1990), 243-249
MSC: Primary 58F11; Secondary 58F18, 58F21
MathSciNet review: 1021217
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Abstract: We consider the rotation set $ \rho (\Phi )$ for a lift $ \Phi = {\{ {\Phi _t}\} _{t \in \mathbb{R}}}$ of a flow $ \varphi = {\{ {\varphi _t}:{\mathbb{T}^2} \to {\mathbb{T}^2}\} _{t \in \mathbb{R}}}$. Our main result is that $ \rho (\Phi )$ consists of either a single point, a segment of a line through 0 with rational slope, or a line segment with irrational slope and one endpoint equal to 0. Any set of one of these types is the rotation set for some flow.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1021217-5
Article copyright: © Copyright 1990 American Mathematical Society