A note about a Morse's conjecture

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In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dime...

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Detalles Bibliográficos
Autor: Huaraca Vargas, Walter T.
Formato: artículo
Fecha de Publicación:2025
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:inglés
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/6624
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624
Nivel de acceso:acceso abierto
Materia:Topological Transitive
Group Action
Metrically Transitive
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spelling A note about a Morse's conjectureA note about a Morse's conjectureA note about a Morse's conjectureHuaraca Vargas, Walter T.Topological TransitiveGroup ActionMetrically TransitiveTopological TransitiveGroup ActionMetrically TransitiveTopological TransitiveGroup ActionMetrically TransitiveIn dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.National University of Trujillo - Academic Department of Mathematics2025-07-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624Selecciones Matemáticas; Vol. 12 No. 01 (2025): January - July; 90 - 96Selecciones Matemáticas; Vol. 12 Núm. 01 (2025): Enero - Julio; 90 - 96Selecciones Matemáticas; v. 12 n. 01 (2025): Janeiro - Julho; 90 - 962411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUenghttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624/6858https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/66242025-07-26T15:43:48Z
dc.title.none.fl_str_mv A note about a Morse's conjecture
A note about a Morse's conjecture
A note about a Morse's conjecture
title A note about a Morse's conjecture
spellingShingle A note about a Morse's conjecture
Huaraca Vargas, Walter T.
Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
title_short A note about a Morse's conjecture
title_full A note about a Morse's conjecture
title_fullStr A note about a Morse's conjecture
title_full_unstemmed A note about a Morse's conjecture
title_sort A note about a Morse's conjecture
dc.creator.none.fl_str_mv Huaraca Vargas, Walter T.
author Huaraca Vargas, Walter T.
author_facet Huaraca Vargas, Walter T.
author_role author
dc.subject.none.fl_str_mv Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
topic Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
Topological Transitive
Group Action
Metrically Transitive
description In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.
publishDate 2025
dc.date.none.fl_str_mv 2025-07-26
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624/6858
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 12 No. 01 (2025): January - July; 90 - 96
Selecciones Matemáticas; Vol. 12 Núm. 01 (2025): Enero - Julio; 90 - 96
Selecciones Matemáticas; v. 12 n. 01 (2025): Janeiro - Julho; 90 - 96
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 13.422088
A note about a Morse's conjecture
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