The action of finite-state tree automorphisms on Bernoulli measures

Rostyslav Kravchenko*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We describe how a finite-state automorphism of a regular rooted tree changes the Bernoulli measure on the boundary of the tree. It turns out that a finite-state automorphism of polynomial growth, as defined by S. Sidki, preserves a measure class of a Bernoulli measure, and we write down the explicit formula for its Radon-Nikodym derivative. On the other hand, the image of the Bernoulli measure under the action of a strongly connected finitestate automorphism is singular to the measure itself.

Original languageEnglish (US)
Pages (from-to)443-451
Number of pages9
JournalJournal of Modern Dynamics
Volume4
Issue number3
DOIs
StatePublished - Jul 2010

Keywords

  • Bernoulli measure
  • Finite automata
  • Markov chain
  • Regular rooted tree

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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