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Hölder exponents of the Green functions of planar polynomial Julia sets

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Hölder exponents of the Green functions of planar polynomial Julia sets

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dc.contributor.author Kosek, Marta [SAP11015773] pl
dc.date.accessioned 2015-03-16T07:32:36Z
dc.date.available 2015-03-16T07:32:36Z
dc.date.issued 2014 pl
dc.identifier.issn 0373-3114 pl
dc.identifier.uri http://ruj.uj.edu.pl/xmlui/handle/item/3825
dc.language eng pl
dc.title Hölder exponents of the Green functions of planar polynomial Julia sets pl
dc.type JournalArticle pl
dc.description.physical 359-368 pl
dc.abstract.en If the Green function gE of a compact set ${E \subset \mathbb{C}}$ is Hölder continuous, then the Hölder exponent of the set E is the supremum over all such α that |g_$E(z)-g_E(w)|\leq M|z-w|^\alpha$,\, $z$, w $\in \mathbb{C}$. We give a lower bound for the Hölder exponent of the Julia sets of polynomials. In particular, we show that there exist totally disconnected planar sets with the Hölder exponent greater than 1/2 as well as fat continua with the boundary nowhere smooth and with the Hölder exponent as close to 1 as we wish. pl
dc.subject.en complex Green function pl
dc.subject.en Hölder continuity pl
dc.subject.en polynomials pl
dc.subject.en iteration pl
dc.subject.en complex dynamics pl
dc.subject.en Julia sets pl
dc.description.volume 193 pl
dc.description.number 2 pl
dc.identifier.doi 10.1007/s10231-012-0278-6 pl
dc.identifier.eissn 1618-1891 pl
dc.title.journal Annali di Matematica Pura ed Applicata pl
dc.language.container eng pl
dc.affiliation Wydział Matematyki i Informatyki : Instytut Matematyki pl
dc.subtype Article pl
dc.rights.original OTHER; inne; ostateczna wersja wydawcy; w momencie opublikowania; 0; pl
.pointsMNiSW [2014 A]: 30


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