3 results found
Verschueren P, Mestel B, 2016, Growth of the Sudler product of sines at the golden rotation number, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol: 433, Pages: 200-226, ISSN: 0022-247X
Verschueren P, Mestel BD, 2014, Fixed points of composition sum operators, JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol: 20, Pages: 1152-1168, ISSN: 1023-6198
Verschueren P, Mestel B, On the growth of Sudler's sine product at the golden rotation number
We study the growth at the golden rotation number of Sudler's sine product.This sequence has been variously studied elsewhere as a skew product of sines,Birkhoff sum, q-Pochhammer symbol (on the unit circle), and restricted Eulerfunction. In particular we study the Fibonacci decimation of the sequence, andprove that the renormalisation subsequence converges to a constant. From thiswe show rigorously that the growth is bounded by power laws. This provides thetheoretical basis to explain recent experimental results reported by Knill andTangerman (Self-similarity and growth in Birkhoff sums for the golden rotation.Nonlinearity, 24(11):3115-3127, 2011).
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