A work on Mirzakhani's earthquakes
"In the 1980s the idea of the earthquake map was introduced by Thurston while he studied low dimension topology. Several mathematicians continued Thurston's studies. In particular, Kerckhoff, who published some of Thurston's unpublished work. But the dynamic properties of the earthqua...
- Autores:
-
Pallejá López, Daniel
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/49383
- Acceso en línea:
- http://hdl.handle.net/1992/49383
- Palabra clave:
- Topología algebraica
Teoría ergódica
Teoría de la medida
Flujos (Sistemas dinámicos diferenciales)
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Artigiani, Mauro1e71b689-1ff0-4b4b-904d-6d49c9d29752500Ferri, Stefanof39df696-f234-4aea-bcb6-0a4a417fb000500Pallejá López, Daniel3af6d0f4-2b6c-48df-9b0c-7c589899a690500Bressler, PaulValdez Lorenzo, José Ferrán2021-03-01T09:14:46Z2021-03-01T09:14:46Z2020http://hdl.handle.net/1992/49383u837599.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/"In the 1980s the idea of the earthquake map was introduced by Thurston while he studied low dimension topology. Several mathematicians continued Thurston's studies. In particular, Kerckhoff, who published some of Thurston's unpublished work. But the dynamic properties of the earthquake map were not described in detail. It was until 2008 when Mirzakhani proved the conjugacy between the earthquake flow and the unipotent flow. The latter one has been better studied, in particular, thanks to Ratner's work. The conjugacy is explained in this document, and it starts for interested new readers exposing the hyperbolic plane. In the latter chapters, the document explains with more detail the natural space of hyperbolic structures on a surface, which is the Teichmüller space. Measured foliations and the dynamics of the earthquake flow are discussed at the end of this work."--Tomado del Formato de Documento de Grado"En los años 1980s Thurston introdujo el concepto de mapa de terremoto durante su estudio de topología en bajas dimensiones. Este mapa fue estudiado entonces por diversos matemáticos como Kerckhoff, pero no tuvo una descripción detallada de sus propiedades dinámicas. Fue hasta 2008 que Mirzakhani mostró que el flujo de terremotos estaba conjugado con el flujo unipotente. Este último, sí ha sido bien entendido, en gran parte gracias a el trabajo de Ratner. Este documento explica esta conjugación abordando el material necesario para lectores nuevos en el tema, empezando desde la geometría del plano hiperbólico, se extiende para hablar con más detalle sobre el espacio de Teichmüller y las foliaciones medibles sobre superficies hiperbólicas, y finaliza definiendo los mapas de terremoto y su conjugación con el flujo unipotente."--Tomado del Formato de Documento de GradoMagíster en MatemáticasMaestría41 hojasapplication/pdfengUniversidad de los AndesMaestría en MatemáticasFacultad de CienciasDepartamento de Matemáticasinstname:Universidad de los Andesreponame:Repositorio Institucional SénecaA work on Mirzakhani's earthquakesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesishttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TMTopología algebraicaTeoría ergódicaTeoría de la medidaFlujos (Sistemas dinámicos diferenciales)MatemáticasPublicationORIGINALu837599.pdfapplication/pdf3961757https://repositorio.uniandes.edu.co/bitstreams/0d98d88d-edfe-452b-b22d-770e66ca8b8b/download64fdba44286b896f9a99b55f9c3c47c2MD51THUMBNAILu837599.pdf.jpgu837599.pdf.jpgIM Thumbnailimage/jpeg6345https://repositorio.uniandes.edu.co/bitstreams/4d4af4f2-58bf-4f63-8608-69135f49771b/download27ea4ff39411c01262981610803bcceaMD55TEXTu837599.pdf.txtu837599.pdf.txtExtracted texttext/plain89642https://repositorio.uniandes.edu.co/bitstreams/714ce9d1-4fe4-4a46-8ea5-bba2520e26f7/download8322075b67e12f24fea073fcca01ae18MD541992/49383oai:repositorio.uniandes.edu.co:1992/493832023-10-10 18:13:56.694http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
| dc.title.es_CO.fl_str_mv |
A work on Mirzakhani's earthquakes |
| title |
A work on Mirzakhani's earthquakes |
| spellingShingle |
A work on Mirzakhani's earthquakes Topología algebraica Teoría ergódica Teoría de la medida Flujos (Sistemas dinámicos diferenciales) Matemáticas |
| title_short |
A work on Mirzakhani's earthquakes |
| title_full |
A work on Mirzakhani's earthquakes |
| title_fullStr |
A work on Mirzakhani's earthquakes |
| title_full_unstemmed |
A work on Mirzakhani's earthquakes |
| title_sort |
A work on Mirzakhani's earthquakes |
| dc.creator.fl_str_mv |
Pallejá López, Daniel |
| dc.contributor.advisor.none.fl_str_mv |
Artigiani, Mauro Ferri, Stefano |
| dc.contributor.author.none.fl_str_mv |
Pallejá López, Daniel |
| dc.contributor.jury.none.fl_str_mv |
Bressler, Paul Valdez Lorenzo, José Ferrán |
| dc.subject.armarc.es_CO.fl_str_mv |
Topología algebraica Teoría ergódica Teoría de la medida Flujos (Sistemas dinámicos diferenciales) |
| topic |
Topología algebraica Teoría ergódica Teoría de la medida Flujos (Sistemas dinámicos diferenciales) Matemáticas |
| dc.subject.themes.none.fl_str_mv |
Matemáticas |
| description |
"In the 1980s the idea of the earthquake map was introduced by Thurston while he studied low dimension topology. Several mathematicians continued Thurston's studies. In particular, Kerckhoff, who published some of Thurston's unpublished work. But the dynamic properties of the earthquake map were not described in detail. It was until 2008 when Mirzakhani proved the conjugacy between the earthquake flow and the unipotent flow. The latter one has been better studied, in particular, thanks to Ratner's work. The conjugacy is explained in this document, and it starts for interested new readers exposing the hyperbolic plane. In the latter chapters, the document explains with more detail the natural space of hyperbolic structures on a surface, which is the Teichmüller space. Measured foliations and the dynamics of the earthquake flow are discussed at the end of this work."--Tomado del Formato de Documento de Grado |
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2020 |
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2020 |
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2021-03-01T09:14:46Z |
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2021-03-01T09:14:46Z |
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Trabajo de grado - Maestría |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/masterThesis |
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Text |
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http://purl.org/redcol/resource_type/TM |
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http://hdl.handle.net/1992/49383 |
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u837599.pdf |
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http://hdl.handle.net/1992/49383 |
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u837599.pdf instname:Universidad de los Andes reponame:Repositorio Institucional Séneca repourl:https://repositorio.uniandes.edu.co/ |
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eng |
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41 hojas |
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Universidad de los Andes |
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Maestría en Matemáticas |
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Facultad de Ciencias |
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Departamento de Matemáticas |
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