Bernoulli convolutions and 1D dynamics

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

DOI

https://doi.org/10.1088/0951-7715/28/11/3921

ISSN

0951-7715

Type

Journal article

Rights

© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at iopscience.iop.org / https://dx.doi.org/10.1088/0951-7715/28/11/3921

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/9629