Partial classification of Lorenz knots: Syllable permutations of torus knots words
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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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1799133409824473088 |