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 >= 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 generalizes a conjecture of Thurston for quadratic polynomials.

40 pages, 11 figures

References in corpus (4)

• Core entropy and biaccessibility of quadratic polynomials
• Core entropy of quadratic polymonials
• Criterion for rays landing together
• The local Hoelder exponent for the entropy of real unimodal maps

Cited by in corpus (1)

• Perturbations of graphs for Newton maps