Polynomials with core entropy zero

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 M d . The characterizations define several quantities which measure the complexities of polynomials with core entropy zero. We show that these measures are all comparable.