Maximizing Core Entropy

Jacob Kewarth

dynamical systems

Maximizing Core Entropy

arXiv:2607.14933

summary

The paper investigates the core entropy function on the space of degree‑d primitive majors—a combinatorial model for degree‑d polynomials—identifying the global maxima and describing the maximal set on the unicritical stratum.

Abstract

Here we study the core entropy function $h : P M (d) \to R$ defined on the space of degree $d$ primitive majors, a combinatorial model for the space of degree $d$ polynomials. In particular, we introduce techniques to classify the global maximum for each $d$ and the maxima along certain strata. We show that there are $d - 1$ global maxima over all of $P M (d)$ and that the maxima on the unicritical stratum is a Cantor set.

Topics & keywords

#core entropy #primitive majors #polynomial dynamics #entropy maximization #unicritical stratumcore entropyprimitive majorsglobal maximumCantor setunicritical stratum