Filled Julia Sets of Chebyshev Polynomials

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

*Corresponding author

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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⊂ 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.

Originalsprog Engelsk Journal of Geometric Analysis 31 12 12250-12263 14 1050-6926 https://doi.org/10.1007/s12220-021-00716-y Udgivet - dec. 2021

Emneord

• Chebyshev polynomials
• Green’s function
• Julia set