Finite orbits in multivalued maps and Bernoulli convolutions

Christoph Bandt, Rüdiger Zeller

Published 2015-09-29Version 1

We consider multivalued maps from a real interval onto itself. Their finite orbits generate Markov partitions, have a certain growth rate and include points with exceptional values of local dimension. Usually, there are no network-like finite orbits but for Pisot parameters, there are many of them. Bernoulli convolutions are studied as a parametric family, with change points generated by certain finite orbits. Among others, we show that certain quantiles of the Bernoulli measures are defined by smooth curves.