Polynomials with core entropy zero

TL;DR

This paper characterizes polynomials with core entropy zero, showing they are precisely those in the degree d main molecule, and introduces measures to quantify their complexity, demonstrating their comparability.

Contribution

It provides multiple characterizations of polynomials with core entropy zero and links them to the degree d main molecule, advancing understanding of their structure.

Findings

Polynomials with core entropy zero are exactly those in the degree d main molecule.

Several complexity measures for these polynomials are introduced and shown to be comparable.

Characterizations help in understanding the structure and classification of such polynomials.

Abstract

This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule. The characterizations define several quantities which measure the complexities of polynomials with core entropy zero. We show that these measures are all comparable.