Filled Julia sets of Chebyshev polynomials

DOI10.1007/s12220-021-00716-yzbMath1485.37043arXiv2106.06392OpenAlexW3175999906WikidataQ122167049 ScholiaQ122167049MaRDI QIDQ2665604

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

Publication date: 19 November 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.06392

zbMATH Keywords

Chebyshev polynomialsGreen's functionJulia set

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Cites Work

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• Asymptotics of Chebyshev polynomials. I: Subsets of \({\mathbb {R}}\)
• Szegő-Widom asymptotics of Chebyshev polynomials on circular arcs
• Julia sets of orthogonal polynomials
• Asymptotics of Chebyshev polynomials. IV: Comments on the complex case
• Weak limits of the measures of maximal entropy for orthogonal polynomials
• Invariant sets under iteration of rational functions
• Extremal polynomials associated with a system of curves in the complex plane
• Orthogonal polynomials associated with invariant measures on Julia sets
• Chebyshev polynomials on circular arcs

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