The core entropy for polynomials of higher degree

2017/03/25 by Yan Gao, Gao, Yan, Giulio Tiozzo +1 · 1 citation
Mathematics · #37B40 #37E25 #37F20 #37F45 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1703.08703

openalex publication_date 2017/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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