arXiv subjects

Renee Oldfield

Publications and source records attributed to Renee Oldfield.

2 recordsLinked to original sources

arXiv2026

The transition between synchronization and chaos for random Blaschke products

In this paper, we establish sufficient conditions for which a class of random circle maps, the so-called random Blaschke products, exhibits either synchronization or chaotic dynamics. We also establish necessary and sufficient conditions for such systems to have a unique random fixed point attractor in the unit disc. As an example, for a class of two map cocycles, we identify the random physical measures as a parameter is varied and investigate the critical value where the dynamics transitions from order to chaos.

math.DS↗

arXiv2025

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

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.

math.DS↗