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Escaping points in the boundaries of Baker domains

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dc.abstract.enWe study dynamical behaviour of points in the boundaries of simply connected Baker domains U for meromorphic maps f, such that f has finite degree on U. We prove that if f on U has hyperbolic or simply parabolic type, then a typical point in the boundary of U (in the sense of harmonic measure) escapes to infinity under iteration. On the contrary, if f on U has doubly parabolic type, then a typical point in the boundary of U (in the sense of harmonic measure) is recurrent, in particular the set of escaping points in the boundary of U has harmonic measure zero. We also present some extensions to the case when f has infinite degree on U.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorJarque, Xavier
dc.contributor.authorKarpińska, Bogusława
dc.contributor.authorFagella, Núria
dc.contributor.authorBarański, Krzysztof
dc.date.accessioned2024-01-24T23:20:30Z
dc.date.available2024-01-24T23:20:30Z
dc.date.issued2019
dc.description.financeNie dotyczy
dc.description.number2
dc.description.volume137
dc.identifier.doi10.1007/S11854-019-0011-0
dc.identifier.issn0021-7670
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/106381
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s11854-019-0011-0
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofJournal d'Analyse Mathematique
dc.relation.pages679-706
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enJulia set, meromorphic function, Baker domain, harmonic measure
dc.subject.plzbiór Julii, funkcje meromorficzne, dziedzina Bakera, miara harmoniczna
dc.titleEscaping points in the boundaries of Baker domains
dc.typeJournalArticle
dspace.entity.typePublication