Bernoulli convolutions and 1D dynamics
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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.
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
© 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