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Filled Julia Sets of Chebyshev Polynomials

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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 \(K\subset {\mathbb C}\) 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.

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Authors and Affiliations

  1. Centre for Mathematical Sciences, Lund University, Box 118, 22100, Lund, Sweden

    Jacob Stordal Christiansen

  2. DTU Compute, Technical University of Denmark, Build. 303B, 2800 Kgs, Lyngby, Denmark

    Christian Henriksen

  3. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Henrik Laurberg Pedersen

  4. Department of Science and Environment, Roskilde University, 4000, Roskilde, Denmark

    Carsten Lunde Petersen

Authors
  1. Jacob Stordal Christiansen
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  2. Christian Henriksen
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  3. Henrik Laurberg Pedersen
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  4. Carsten Lunde Petersen
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Correspondence to Christian Henriksen.

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Christiansen, J.S., Henriksen, C., Pedersen, H.L. et al. Filled Julia Sets of Chebyshev Polynomials. J Geom Anal 31, 12250–12263 (2021). https://doi.org/10.1007/s12220-021-00716-y

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  • DOI: https://doi.org/10.1007/s12220-021-00716-y

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