Combinatorial and probabilistic properties of systems of numeration

Guy Barat, Peter Grabner

Research output: Contribution to journalArticlepeer-review


Let be a strictly increasing sequence of positive integers with . We study the system of numeration defined by this sequence by looking at the corresponding compactification of and the extension of the addition-by-one map on (the 'odometer'). We give sufficient conditions for the existence and uniqueness of -invariant measures on in terms of combinatorial properties of.
Original languageEnglish
Pages (from-to)422-457
JournalErgodic theory and dynamical systems
Issue number2
Publication statusPublished - 2016


  • odometers

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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