One-parameter families of circle diffeomorphisms with strictly monotone rotation number

Kiran Avinash Parkhe*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We show that if f: S1 × S1 → S1 × S1 is C2, with f(x, t) = (ft(x), t), and the rotation number of ft is equal to t for all t ∈ S1, 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 ft is t is weakened to say that the rotation number is strictly monotone in t.

Original languageEnglish (US)
Pages (from-to)4327-4337
Number of pages11
JournalProceedings of the American Mathematical Society
Volume141
Issue number12
DOIs
StatePublished - Oct 4 2013

Keywords

  • Rotation number
  • Strict monotonicity
  • Topological conjugacy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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