Copy the page URI to the clipboard
Verschueren, Paul and Mestel, Ben
(2016).
DOI: https://doi.org/10.1016/j.jmaa.2015.06.014
Abstract
We study the growth at the golden rotation number of the function sequence
. This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, q-Pochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence
, namely the subsequence
for Fibonacci numbers
, and prove that this renormalisation subsequence converges to a constant. From this we show rigorously that the growth of
is bounded by power laws. This provides the theoretical basis to explain recent experimental results reported by Knill and Tangerman (Self-similarity and growth in Birkhoff sums for the golden rotation. Nonlinearity, 24(11):3115-3127,
2011).
Viewing alternatives
Download history
Metrics
Public Attention
Altmetrics from AltmetricNumber of Citations
Citations from DimensionsItem Actions
Export
About
- Item ORO ID
- 43460
- Item Type
- Journal Item
- ISSN
- 0022-247X
- Extra Information
- 2015 is an estimated publication date.
- Keywords
- Asymptotic growth, renormalisation, self-similarity, sine product
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Depositing User
- Benjamin Mestel