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Transactions of the American Mathematical Society

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On Thurston's core entropy algorithm


Author: Yan Gao
Journal: Trans. Amer. Math. Soc. 373 (2020), 747-776
MSC (2010): Primary 37B40, 37F10, 37F20
DOI: https://doi.org/10.1090/tran/7122
Published electronically: October 17, 2019
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Abstract: The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant extending topological entropy for real maps to complex polynomials, whence providing a new tool to study the parameter space of polynomials. The base is a combinatorial algorithm allowing for the computation of the core entropy given by Thurston but without supplying a proof. In this paper, we will describe his algorithm and prove its validity.


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Additional Information

Yan Gao
Affiliation: Mathematical School of Sichuan University, Chengdu 610064, People’s Republic of China
Email: gyan@scu.edu.cn

DOI: https://doi.org/10.1090/tran/7122
Keywords: Core entropy, Hubbard tree, critical portrait, polynomial, complex dynamics.
Received by editor(s): March 26, 2016
Received by editor(s) in revised form: August 17, 2016, and November 4, 2016
Published electronically: October 17, 2019
Additional Notes: The author was partially supported by NSFC grant No. 11501383.
Article copyright: © Copyright 2019 American Mathematical Society