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Bernoulli convolutions and 1D dynamics

Research output: Contribution to journalArticle

Author(s)

Thomas Michael William Kempton, Tomas Persson

School/Research organisations

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.

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Details

Original languageEnglish
Pages (from-to)3921-3934
JournalNonlinearity
Volume28
Issue number11
DOIs
Publication statusPublished - 8 Oct 2015

    Research areas

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

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