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.

中文翻译：

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切比雪夫多项式的填充 Julia 集

我们研究了非极性紧致集合\(K\subset {\mathbb C}\) 的对偶 Chebyshev 多项式序列的 Julia 集和填充 Julia 子序列的可能 Hausdorff 限制，并将这些限制与K进行比较。此外，我们证明了K 的对偶 Chebyshev 多项式序列的最大熵度量弱收敛于K上的均衡度量。