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 confirms a conjecture of W. Thurston.
The core entropy for polynomials of higher degree / Gao, Y.; Tiozzo, G.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 24:7(2022), pp. 2555-2603. [10.4171/JEMS/1154]
The core entropy for polynomials of higher degree
Tiozzo G.
2022
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 confirms a conjecture of W. Thurston.File allegati a questo prodotto
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