Invariant density functions of random β-transformations

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Abstract

We consider the random -transformation introduced by Dajani and Kraaikamp [Random -expansions. Ergod. Th. & Dynam. Sys. 23 (2003), 461-479], which is defined on . We give an explicit formula for the density function of a unique -invariant probability measure absolutely continuous with respect to the product measure , where is the -Bernoulli measure on and is the normalized Lebesgue measure on . We apply the explicit formula for the density function to evaluate its upper and lower bounds and to investigate its continuity as a function of the two parameters and .

Original languageEnglish
Pages (from-to)1099-1120
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number4
DOIs
Publication statusPublished - 2019 Apr 1
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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