A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j

Detalhes bibliográficos
Autor(a) principal: Arteaga,Carlos
Data de Publicação: 2012
Outros Autores: Alves,Alexandre
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000100002
Resumo: Let j be a positive integer. For each integer n &gt; j we consider the connectedness locus Mn of the family of polynomials Pc(z) = z n - cz n-j, where c is a complex parameter. We prove that lim n→&#8734; Mn = D in the Hausdorff topology, where D is the unitary closed disk {c;|c|<1}.
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spelling A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-jJulia setconnectedness locushyperbolic componentsprincipal componentsLet j be a positive integer. For each integer n &gt; j we consider the connectedness locus Mn of the family of polynomials Pc(z) = z n - cz n-j, where c is a complex parameter. We prove that lim n→&#8734; Mn = D in the Hausdorff topology, where D is the unitary closed disk {c;|c|<1}.Academia Brasileira de Ciências2012-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000100002Anais da Academia Brasileira de Ciências v.84 n.1 2012reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652012005000004info:eu-repo/semantics/openAccessArteaga,CarlosAlves,Alexandreeng2012-05-22T00:00:00Zoai:scielo:S0001-37652012000100002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2012-05-22T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
title A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
spellingShingle A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
Arteaga,Carlos
Julia set
connectedness locus
hyperbolic components
principal components
title_short A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
title_full A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
title_fullStr A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
title_full_unstemmed A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
title_sort A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j
author Arteaga,Carlos
author_facet Arteaga,Carlos
Alves,Alexandre
author_role author
author2 Alves,Alexandre
author2_role author
dc.contributor.author.fl_str_mv Arteaga,Carlos
Alves,Alexandre
dc.subject.por.fl_str_mv Julia set
connectedness locus
hyperbolic components
principal components
topic Julia set
connectedness locus
hyperbolic components
principal components
description Let j be a positive integer. For each integer n &gt; j we consider the connectedness locus Mn of the family of polynomials Pc(z) = z n - cz n-j, where c is a complex parameter. We prove that lim n→&#8734; Mn = D in the Hausdorff topology, where D is the unitary closed disk {c;|c|<1}.
publishDate 2012
dc.date.none.fl_str_mv 2012-03-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000100002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000100002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652012005000004
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.84 n.1 2012
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
instacron_str ABC
institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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