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arXiv · 1703.08703

The core entropy for polynomials of higher degree

Yan Gao·Giulio Tiozzo
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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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Yan Gao, Giulio Tiozzo. 2017-03-25. The core entropy for polynomials of higher degree. https://arxiv.org/abs/1703.08703

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