Core entropy of polynomials with a critical point of maximal order

Domingo González; Gamaliel Blé

doi:10.3934/dcds.2019005

Article Contents

2019, Volume 39, Issue 1: 115-130. Doi: 10.3934/dcds.2019005

This issue Previous Article Phase portraits of linear type centers of polynomial Hamiltonian systems with Hamiltonian function of degree 5 of the form

$ H = H_1(x)+H_2(y)$

Next Article The mean field analysis of the Kuramoto model on graphs Ⅰ. The mean field equation and transition point formulas

Core entropy of polynomials with a critical point of maximal order

Domingo González^, and
Gamaliel Blé

División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Carr. Cunduacán-Jalpa Km 1, Cunduacán Tabasco, México

* Corresponding author
* Corresponding author

Received: August 31, 2017

Revised: June 30, 2018

Published: December 2018

The first author is supported by CONACY CB-2012/181247 and 488419/278289

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Abstract

This paper discusses some properties of the topological entropy of the systems generated by polynomials of degree $ d$ with two critical points. A partial order in the parameter space is defined. The monotonicity of the topological entropy of postcritically finite polynomials of degree $ d$ acting on Hubbard tree is generalized.

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Mathematics Subject Classification: Primary: 37F10, 37B40; Secondary: 28D20, 37F45.

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Figure 1. Connectedness locus for $d = 4$ and $d = 5$

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Figure 2. Filled Julia set and intervals of angles of $P_a$

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