Filled Julia sets of Chebyshev polynomials

Filled Julia sets of Chebyshev polynomials

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 in C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev poly...

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Hauptverfasser: Christiansen, Jacob Stordal, Henriksen, Christian, Pedersen, Henrik Laurberg, Petersen, Carsten Lunde
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Complex Variables
Mathematics - Dynamical Systems
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Zusammenfassung: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 in 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.
DOI:10.48550/arxiv.2106.06392