Bernoulli convolutions and 1D dynamics
Abstract
We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.
Citation
Kempton , T M W & Persson , T 2015 , ' Bernoulli convolutions and 1D dynamics ' , Nonlinearity , vol. 28 , no. 11 , pp. 3921-3934 . https://doi.org/10.1088/0951-7715/28/11/3921
Publication
Nonlinearity
Status
Peer reviewed
ISSN
0951-7715Type
Journal article
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