Bernoulli convolutions and 1D dynamics

Thomas Michael William Kempton, Tomas Persson

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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.

Original languageEnglish
Pages (from-to)3921-3934
Issue number11
Publication statusPublished - 8 Oct 2015


  • Bernoulli convolutions
  • 1D dynamics
  • Ergodic theory
  • Transfer operators


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