The core entropy for polynomials of higher degree

Abstract

As defined by W. Thurston, the core entropy of a polynomial is the entropy of the restriction to its Hubbard tree. For each $d\ge 2$, we study the core entropy as a function on the parameter space of polynomials of degree $d$, and prove it varies continuously both as a function of the combinatorial data and of the coefficients of the polynomials. This confirms a conjecture of W. Thurston.