Self-similar measures and their images under automatic maps

The notion of self-similar measure mimics the notion of self-similar group. Self-similar measures have interesting properties and various applications. Bernoulli and Markov measures are self-similar. After introduction to the theory of self-similar measures I will discuss how they behave under the coding maps, including the automatic maps.
Based on joint results with Roman Kogan and Yaroslav Vorobets.