POLYNOMIALS WITH CORE ENTROPY ZERO

Yusheng Luo; Insung Park

doi:10.3934/jmd.2026002

POLYNOMIALS WITH CORE ENTROPY ZERO

Yusheng Luo
, Insung Park

Mathematical Science Institute

Cornell University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule M_d. The characterizations define several comparable quantities which measure the complexities of polynomials with core entropy zero and allow us to have a better understanding of the structure of the main molecule in higher degrees.

Original language	English
Pages (from-to)	73-132
Number of pages	60
Journal	Journal of Modern Dynamics
Volume	22
DOIs	https://doi.org/10.3934/jmd.2026002
State	Published - 2026

Keywords

Complex dynamics
core entropy
main molecule

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10.3934/jmd.2026002

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title = "POLYNOMIALS WITH CORE ENTROPY ZERO",

abstract = "This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule Md. The characterizations define several comparable quantities which measure the complexities of polynomials with core entropy zero and allow us to have a better understanding of the structure of the main molecule in higher degrees.",

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doi = "10.3934/jmd.2026002",

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AU - Luo, Yusheng

AU - Park, Insung

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N2 - This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule Md. The characterizations define several comparable quantities which measure the complexities of polynomials with core entropy zero and allow us to have a better understanding of the structure of the main molecule in higher degrees.

AB - This paper studies polynomials with core entropy zero. We give several characterizations of polynomials with core entropy zero. In particular, we show that a degree d post-critically finite polynomial f has core entropy zero if and only if f is in the degree d main molecule Md. The characterizations define several comparable quantities which measure the complexities of polynomials with core entropy zero and allow us to have a better understanding of the structure of the main molecule in higher degrees.

KW - Complex dynamics

KW - core entropy

KW - main molecule

UR - https://www.scopus.com/pages/publications/105029305701

U2 - 10.3934/jmd.2026002

DO - 10.3934/jmd.2026002

M3 - Article

AN - SCOPUS:105029305701

SN - 1930-5311

VL - 22

SP - 73

EP - 132

JO - Journal of Modern Dynamics

JF - Journal of Modern Dynamics

ER -

POLYNOMIALS WITH CORE ENTROPY ZERO

Abstract

Keywords

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