The conjugating map for commutative groups of circle diffeomorphisms

Bryna Kra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


For a single aperiodic, orientation preserving diffeomorphism on the circle, all known local results on the differentiability of the conjugating map are also known to be global results. We show that this does not hold for commutative groups of diffeomorphisms. Given a set of rotation numbers, we construct commuting diffeomorphisms in C2-ε for all ε > 0 with these rotation numbers that are not conjugate to rotations. On the other hand, we prove that for a commutative subgroup ℱ ⊂ C1+β, 0 < β < 1, containing diffeomorphisms that are perturbations of rotations, a conjugating map h exists as long as the rotation numbers of this subset jointly satisfy a Diophantine condition.

Original languageEnglish (US)
Pages (from-to)303-316
Number of pages14
JournalIsrael Journal of Mathematics
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Mathematics(all)


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