Filled Julia Sets of Chebyshev Polynomials

Jacob Stordal Christiansen; Christian Henriksen; Henrik Laurberg Pedersen; Carsten Lunde Petersen

doi:10.1007/s12220-021-00716-y

Filled Julia Sets of Chebyshev Polynomials

Jacob Stordal Christiansen, Christian Henriksen^*, Henrik Laurberg Pedersen, Carsten Lunde Petersen

^*Corresponding author for this work

Department of Science and Environment

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev polynomials of K converges weak* to the equilibrium measure on K.

Original language	English
Journal	Journal of Geometric Analysis
Volume	31
Issue number	12
Pages (from-to)	12250-12263
Number of pages	14
ISSN	1050-6926
DOIs	https://doi.org/10.1007/s12220-021-00716-y
Publication status	Published - Dec 2021

Keywords

Chebyshev polynomials
Green’s function
Julia set

Link to document

10.1007/s12220-021-00716-y

Chebyshev_7.3Submitted manuscript, 1.59 MB

Cite this

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title = "Filled Julia Sets of Chebyshev Polynomials",

abstract = "We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev polynomials of K converges weak* to the equilibrium measure on K.",

keywords = "Chebyshev polynomials, Green{\textquoteright}s function, Julia set, Chebyshev polynomials, Green{\textquoteright}s function, Julia set",

author = "Christiansen, {Jacob Stordal} and Christian Henriksen and Pedersen, {Henrik Laurberg} and Petersen, {Carsten Lunde}",

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AU - Christiansen, Jacob Stordal

AU - Henriksen, Christian

AU - Pedersen, Henrik Laurberg

AU - Petersen, Carsten Lunde

PY - 2021/12

Y1 - 2021/12

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AB - We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev polynomials of K converges weak* to the equilibrium measure on K.

KW - Chebyshev polynomials

KW - Green’s function

KW - Julia set

KW - Chebyshev polynomials

KW - Green’s function

KW - Julia set

U2 - 10.1007/s12220-021-00716-y

DO - 10.1007/s12220-021-00716-y

M3 - Journal article

AN - SCOPUS:85108343519

SN - 1050-6926

VL - 31

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EP - 12263

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JF - Journal of Geometric Analysis

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