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arXiv · 2505.09948

Average measure theoretic entropy for a family of expanding on average random Blaschke products

Cecilia González-Tokman·Renee Oldfield
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Abstract

This work gives a computable formula for the average measure theoretic entropy of a family of expanding on average random Blaschke products, generalizing work by Pujals, Roberts and Shub [Expanding maps of the circle revisited: positive Lyapunov exponents in a rich family. $\textit{Ergodic Theory Dynam. Systems.}$ $\textbf{26}(6)$ $(2006),$ $1931$-$1937$] to the random setting. In doing so, we describe the random invariant measure and associated measure theoretic entropy for a class of admissible random Blaschke products, allowing for maps which are not necessarily expanding and may even have an attracting fixed point.

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Cecilia González-Tokman, Renee Oldfield. 2025-05-15. Average measure theoretic entropy for a family of expanding on average random Blaschke products. https://arxiv.org/abs/2505.09948

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