### Abstract

We show that if f: S^{1} × S^{1} → S^{1} × 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 ∈ S^{1}, then f is topologically conjugate to the linear Dehn twist of the torus. 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.

Original language | English (US) |
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Pages (from-to) | 4327-4337 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 141 |

Issue number | 12 |

DOIs | |

State | Published - Oct 4 2013 |

### Keywords

- Rotation number
- Strict monotonicity
- Topological conjugacy

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Parkhe, K. A. (2013). One-parameter families of circle diffeomorphisms with strictly monotone rotation number.

*Proceedings of the American Mathematical Society*,*141*(12), 4327-4337. https://doi.org/10.1090/S0002-9939-2013-11699-0