Partial classification of Lorenz knots: Syllable permutations of torus knots words

Detalhes bibliográficos
Autor(a) principal: Gomes, Paulo
Data de Publicação: 2015
Outros Autores: Franco, Nuno, Silva, Luís
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/6001
Resumo: We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.
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spelling Partial classification of Lorenz knots: Syllable permutations of torus knots wordsLorenz knotsHyperbolic knotsSymbolic dynamicsWe define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.Elsevier Science BVRCIPLGomes, PauloFranco, NunoSilva, Luís2016-04-15T15:07:29Z2015-06-152015-06-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/6001engGOMES, Paulo; FRANCO, Nuno; SILVA, Luís – Partial classification of Lorenz knots: Syllable permutations of torus knots words. Physica D-Nonlinear Phenomena. ISSN.0167-2789. Vol. 306 (2015), pp. 16-24.0167-278910.1016/j.physd.2015.05.001info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:14Zoai:repositorio.ipl.pt:10400.21/6001Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:12.968593Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Partial classification of Lorenz knots: Syllable permutations of torus knots words
title Partial classification of Lorenz knots: Syllable permutations of torus knots words
spellingShingle Partial classification of Lorenz knots: Syllable permutations of torus knots words
Gomes, Paulo
Lorenz knots
Hyperbolic knots
Symbolic dynamics
title_short Partial classification of Lorenz knots: Syllable permutations of torus knots words
title_full Partial classification of Lorenz knots: Syllable permutations of torus knots words
title_fullStr Partial classification of Lorenz knots: Syllable permutations of torus knots words
title_full_unstemmed Partial classification of Lorenz knots: Syllable permutations of torus knots words
title_sort Partial classification of Lorenz knots: Syllable permutations of torus knots words
author Gomes, Paulo
author_facet Gomes, Paulo
Franco, Nuno
Silva, Luís
author_role author
author2 Franco, Nuno
Silva, Luís
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Gomes, Paulo
Franco, Nuno
Silva, Luís
dc.subject.por.fl_str_mv Lorenz knots
Hyperbolic knots
Symbolic dynamics
topic Lorenz knots
Hyperbolic knots
Symbolic dynamics
description We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.
publishDate 2015
dc.date.none.fl_str_mv 2015-06-15
2015-06-15T00:00:00Z
2016-04-15T15:07:29Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/6001
url http://hdl.handle.net/10400.21/6001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv GOMES, Paulo; FRANCO, Nuno; SILVA, Luís – Partial classification of Lorenz knots: Syllable permutations of torus knots words. Physica D-Nonlinear Phenomena. ISSN.0167-2789. Vol. 306 (2015), pp. 16-24.
0167-2789
10.1016/j.physd.2015.05.001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Science BV
publisher.none.fl_str_mv Elsevier Science BV
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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