# American Institute of Mathematical Sciences

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July  2010, 4(3): 443-451. doi: 10.3934/jmd.2010.4.443

## The action of finite-state tree automorphisms on Bernoulli measures

 1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, United States

Received  October 2009 Revised  July 2010 Published  October 2010

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 finite-state automorphism is singular to the measure itself.
Citation: Rostyslav Kravchenko. The action of finite-state tree automorphisms on Bernoulli measures. Journal of Modern Dynamics, 2010, 4 (3) : 443-451. doi: 10.3934/jmd.2010.4.443
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