One-parameter families of circle diffeomorphisms with strictly monotone rotation number
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- by Kiran Parkhe PDF
- Proc. Amer. Math. Soc. 141 (2013), 4327-4337 Request permission
Abstract:
We show that if $f \colon S^1 \times S^1 \to S^1 \times S^1$ is $C^2$, with $f(x, t) = (f_t(x), t)$, and the rotation number of $f_t$ is equal to $t$ for all $t \in S^1$, then $f$ is topologically conjugate to the linear Dehn twist of the torus $\left ( \begin {smallmatrix} 1&1\\ 0&1 \end {smallmatrix} \right )$. We prove a differentiability result where the assumption that the rotation number of $f_t$ is $t$ is weakened to say that the rotation number is strictly monotone in $t$.References
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Additional Information
- Kiran Parkhe
- Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
- Received by editor(s): December 12, 2011
- Received by editor(s) in revised form: February 7, 2012, and February 14, 2012
- Published electronically: August 22, 2013
- Communicated by: Bryna Kra
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4327-4337
- MSC (2010): Primary 37C15, 37E10, 37E45; Secondary 37C05
- DOI: https://doi.org/10.1090/S0002-9939-2013-11699-0
- MathSciNet review: 3105874