Emma Dinowitz | Searcharxiv

arXiv2026

Point-to-set principles in dynamical systems

In analogy to the point-to-set principle for Hausdorff and packing dimension of Lutz, Lutz, and Mayordomo, we develop a Kolmogorov complexity point-to-set principle framework for upper and lower topological pressure and BS dimension in dynamical systems (and by extension for upper and lower entropy). As a demonstration of this framework we expand upon the Bowen pressure equation results of Climenhaga, as well as prove a pointwise version of the Bowen pressure equation.

math.DS↗

arXiv2025

Growth and Language Complexity of Potentially Positive Elements of Free Groups

A word in a free group is called ``potentially positive'' if it is automorphic to an element which is written with only positive exponents. We will develop automata to analyze properties of potentially positive words. We will use these to give new bounds on the asymptotic growth of potentially positive elements in free groups of 2 to 7 generators. We prove the bounds for $F_2$ are tight, giving the growth function up to a constant multiplier. We use the same tools to show that certain restricted automata cannot recognize the set of potentially positive elements.

math.GR↗