Herman rings of blaschke products of degree 3

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Let Fa,λ be the Blaschke product of the form F a,λ = λz2((z - a)/(1 āz)) and α denote an irrational number satisfying the Brjuno condition. Henriksen [1997] showed that for any α there exists a constant a0 ≧ 3 and a continuous function λ(a) such that Fa,λ(a) possesses an Herman ring and also that modulus M(a) of the Herman ring approaches 0 as a approaches a0. It is remarked that the question whether a0 = 3 holds or not is open. According to the idea of Fagella and Geyer [2003] we can show that for a certain set of irrational rotation numbers, a0 is strictly larger than 3.

Original languageEnglish
Pages (from-to)445-451
Number of pages7
JournalInternational Journal of Bifurcation and Chaos
Issue number1
Publication statusPublished - Jan 2009


  • Blaschke product
  • Herman ring


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