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ŁS condition for filled Julia sets in $$\mathbb {C}$$C
2018
Annali di Matematica Pura ed Applicata
In this article, we derive an inequality of Łojasiewicz-Siciak type for certain sets arising in the context of the complex dynamics in dimension 1. More precisely, if we denote by dist the euclidian distance in C, we show that the Green function G_K of the filled Julia set K of a polynomial such that K≠∅ satisfies the so-called ŁS condition G_A≥ c· dist(·, K)^c' in a neighborhood of K, for some constants c,c'>0. Relatively few examples of compact sets satisfying the ŁS condition are known. Our
doi:10.1007/s10231-018-0752-x
fatcat:dxuivw4hprc3ngzvfndzjhuvsi