Julia sets are uniformly perfect

Detalhes bibliográficos
Autor(a) principal: Mane, Ricardo
Data de Publicação: 1992
Outros Autores: Rocha, Luiz Fernando Carvalho da
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/27484
Resumo: We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin's theorem.
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spelling Mane, RicardoRocha, Luiz Fernando Carvalho da2011-01-26T05:59:12Z19920002-9939http://hdl.handle.net/10183/27484000054805We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin's theorem.application/pdfengProceedings of the American Mathematical Society. Providence, RI. Vol. 116, no. 1 (sept. 1992), p. 251-257.Teoria ergódicaEntropia : Medidas harmonicasConjuntos de juliaJulia sets are uniformly perfectEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000054805.pdf000054805.pdfTexto completo (inglês)application/pdf147305http://www.lume.ufrgs.br/bitstream/10183/27484/1/000054805.pdf9c91adeb9082cdf1e79830f509c41f99MD51TEXT000054805.pdf.txt000054805.pdf.txtExtracted Texttext/plain14060http://www.lume.ufrgs.br/bitstream/10183/27484/2/000054805.pdf.txt26b3018cd0fe1f09badbdea1c75de4e8MD52THUMBNAIL000054805.pdf.jpg000054805.pdf.jpgGenerated Thumbnailimage/jpeg1776http://www.lume.ufrgs.br/bitstream/10183/27484/3/000054805.pdf.jpg0b676e1f6814b02591c3e3d50225baf3MD5310183/274842021-06-26 04:38:42.927398oai:www.lume.ufrgs.br:10183/27484Repositório InstitucionalPUBhttps://lume.ufrgs.br/oai/requestlume@ufrgs.bropendoar:2021-06-26T07:38:42Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Julia sets are uniformly perfect
title Julia sets are uniformly perfect
spellingShingle Julia sets are uniformly perfect
Mane, Ricardo
Teoria ergódica
Entropia : Medidas harmonicas
Conjuntos de julia
title_short Julia sets are uniformly perfect
title_full Julia sets are uniformly perfect
title_fullStr Julia sets are uniformly perfect
title_full_unstemmed Julia sets are uniformly perfect
title_sort Julia sets are uniformly perfect
author Mane, Ricardo
author_facet Mane, Ricardo
Rocha, Luiz Fernando Carvalho da
author_role author
author2 Rocha, Luiz Fernando Carvalho da
author2_role author
dc.contributor.author.fl_str_mv Mane, Ricardo
Rocha, Luiz Fernando Carvalho da
dc.subject.por.fl_str_mv Teoria ergódica
Entropia : Medidas harmonicas
Conjuntos de julia
topic Teoria ergódica
Entropia : Medidas harmonicas
Conjuntos de julia
description We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin's theorem.
publishDate 1992
dc.date.issued.fl_str_mv 1992
dc.date.accessioned.fl_str_mv 2011-01-26T05:59:12Z
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dc.relation.ispartof.pt_BR.fl_str_mv Proceedings of the American Mathematical Society. Providence, RI. Vol. 116, no. 1 (sept. 1992), p. 251-257.
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