Bernoulli convolutions and 1D dynamics

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Abstract

We describe a family phi(lambda) 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 phi(lambda) and give some numerical evidence to suggest values of lambda for which phi(lambda) may be piecewise convex.

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Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • bernoulli convolutions, tent maps, absolutely continuous invariant, measures
Original languageEnglish
Pages (from-to)3921-3934
JournalNonlinearity
Volume28
Issue number11
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes