Rotation sets of toral flows
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- by John Franks and Michał Misiurewicz PDF
- Proc. Amer. Math. Soc. 109 (1990), 243-249 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 243-249
- MSC: Primary 58F11; Secondary 58F18, 58F21
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021217-5
- MathSciNet review: 1021217