Hölder exponents of the Green functions of planar polynomial Julia sets

2014
journal article
article
3
cris.lastimport.wos2024-04-10T02:23:49Z
dc.abstract.enIf 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.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorKosek, Marta - 129178 pl
dc.date.accessioned2015-03-16T07:32:36Z
dc.date.available2015-03-16T07:32:36Z
dc.date.issued2014pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number2pl
dc.description.physical359-368pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume193pl
dc.identifier.doi10.1007/s10231-012-0278-6pl
dc.identifier.eissn1618-1891pl
dc.identifier.issn0373-3114pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/3825
dc.languageengpl
dc.language.containerengpl
dc.rights*
dc.rights.licenceCC-BY
dc.rights.uri*
dc.share.typeinne
dc.subject.encomplex Green functionpl
dc.subject.enHölder continuitypl
dc.subject.enpolynomialspl
dc.subject.eniterationpl
dc.subject.encomplex dynamicspl
dc.subject.enJulia setspl
dc.subtypeArticlepl
dc.titleHölder exponents of the Green functions of planar polynomial Julia setspl
dc.title.journalAnnali di Matematica Pura ed Applicatapl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-10T02:23:49Z
dc.abstract.enpl
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.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Kosek, Marta - 129178
dc.date.accessioned
2015-03-16T07:32:36Z
dc.date.available
2015-03-16T07:32:36Z
dc.date.issuedpl
2014
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.numberpl
2
dc.description.physicalpl
359-368
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
193
dc.identifier.doipl
10.1007/s10231-012-0278-6
dc.identifier.eissnpl
1618-1891
dc.identifier.issnpl
0373-3114
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/3825
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
dc.rights.licence
CC-BY
dc.rights.uri*
dc.share.type
inne
dc.subject.enpl
complex Green function
dc.subject.enpl
Hölder continuity
dc.subject.enpl
polynomials
dc.subject.enpl
iteration
dc.subject.enpl
complex dynamics
dc.subject.enpl
Julia sets
dc.subtypepl
Article
dc.titlepl
Hölder exponents of the Green functions of planar polynomial Julia sets
dc.title.journalpl
Annali di Matematica Pura ed Applicata
dc.typepl
JournalArticle
dspace.entity.type
Publication

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