Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.

ilustraciones

Autores:: Giraldo Galeano, Oscar Iván

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2021

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
dc.title.translated.eng.fl_str_mv	End periodic homeomorphisms and generalized pseudo-Anosov homeomorphisms
title	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
spellingShingle	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados. 510 - Matemáticas Geometría Euclidiana Euclidean geometry Foliations (mathematics) Foliaciones (Matemáticas Superficie final periódica Homeomorfismo final periódico Homeomorfismo Pseudo-Anosov Generalizado Entropía cero End periodic surfaces End periodic homeomorphisms Generalized Pseudo-Anosov homeomorphisms Zero entropy
title_short	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
title_full	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
title_fullStr	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
title_full_unstemmed	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
title_sort	Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.
dc.creator.fl_str_mv	Giraldo Galeano, Oscar Iván
dc.contributor.advisor.none.fl_str_mv	Rodríguez Nieto, José Gregorio
dc.contributor.author.none.fl_str_mv	Giraldo Galeano, Oscar Iván
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas
topic	510 - Matemáticas Geometría Euclidiana Euclidean geometry Foliations (mathematics) Foliaciones (Matemáticas Superficie final periódica Homeomorfismo final periódico Homeomorfismo Pseudo-Anosov Generalizado Entropía cero End periodic surfaces End periodic homeomorphisms Generalized Pseudo-Anosov homeomorphisms Zero entropy
dc.subject.lem.none.fl_str_mv	Geometría Euclidiana
dc.subject.lemb.none.fl_str_mv	Euclidean geometry Foliations (mathematics) Foliaciones (Matemáticas
dc.subject.proposal.spa.fl_str_mv	Superficie final periódica Homeomorfismo final periódico Homeomorfismo Pseudo-Anosov Generalizado Entropía cero
dc.subject.proposal.eng.fl_str_mv	End periodic surfaces End periodic homeomorphisms Generalized Pseudo-Anosov homeomorphisms Zero entropy
description	ilustraciones
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-10-11T16:45:38Z
dc.date.available.none.fl_str_mv	2021-10-11T16:45:38Z
dc.date.issued.none.fl_str_mv	2021
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
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dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
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identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.references.spa.fl_str_mv	[Ahl] Ahlfors L, Conformal invariants: topics in geometric function theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co. New York (1973) MR0357743 [Be-Ha] Bestvida M, Handel M. 1995. Train-Tracks for surfacenhomeomorphisms. Topology Vol. 34. No. I, pp. 109-MO,1995 [deC-H1] de Carvalho A, Hall T. 2004. Unimodal generalized pseudo-Anosov maps. Geom Topol 8:1127-1188. [deC2] de Carvalho A. 2005. Extensions, quotients and genelized pseudo-Anosov maps. AMS Proc. Sympos. Pure Math 75:315-338. [deC-P3] de Carvalho A, Patermain M. 2004. Monotone quotients of surface diffeomorphisms. Math. Res. Lett 10:603-619 [deC-H4] de Carvalho A, Hall T. 2010. Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences, arXiv:1010.3448. [Fe1] Fenley S. 1990. Endperiodic surface homeomorphisms and 3-manifolds. Math Z. 224:1-24 [Fe2] Fenley S. 1992. Asymptotic properties of depth one foliations in hyperbolic 3-manifolds. Jour. Diff. Geo. 36:269-313. [Forster] O. Forster, Riemann Surfaces, Springer-Verlag, 1981. [Ca-Bl] Casson A, Bleiler S. 1988. Automorphisms of surface after Nielsen and Thurston. London Math. Soc. student Text 9 Cambridge Univ. Press. [Ca-Co1] Cantwell J, Conlon L. 2011. Handel-Miller theory and finite depth foliations, arXiv:1006.4525. [Ca-Co2] Cantwell J, Conlon L. 2010. Examples of endperiodic maps, arXiv:1008.2549 [Ca-Co3] Cantwell J, Conlon L. 1999. Foliations cones. Geometry and Topology Monographs, Proceedings of the Kirbyfest. 2: 35-86. [Ca-Co4] Cantwell J, Conlon L. 2000. Foliations I. AMS [Ch-Ga-La] Chamanara R, Gardiner F, Lakic N. 2006. A hyperelliptic realization of the horseshoe and baker maps. Ergod. Th. and Dynam. Sys. 26:1749-1768. Fle] Fleming, W. “Nondegenerate surfaces of finite topological type.” Transactions of the American Mathematical Society 90 (1959): 323-335. [Ghys] E. Ghys, Laminations par surfaces de Riemann, Panorames e Synthesis, SMF, 2000. [Ga-La] Gardiner F, Lakic N. 2000. Quasiconformal Teichmuller Theory. AMS. Math. Sur. and Monog. Vol 76. [Ga-Fre] Gardiner F,Frederick P. Measured foliations and the minimal norm property for quadratic differentials. Acta Math., 152(1-2):57-76, 1984. [Gi-Fi] Gilbert H, Ulrich H. Introduction to the geometry of foliations. Part A. Friedr. Vieweg and Sohn, Braunschweig, second edition, 1986. Foliations on compact surfaces, fundamentals for arbitrary codimension, and holonomy Gaspard] Gaspard, P. (1998). Chaos, Scattering and Statistical Mechanics (Cambridge Nonlinear Science Series). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511628856 [Hu-Ma] Hubbard J, Masur H. 1979. Quadratic differentials and foliations. Acta Math. 142:221-274. [Mi] Sappala M. Foliations and Quadratic Differentials of Riemann Surface. [St] Strebel K. 1988. On the extremality and unique extremality of certain Teichmuller mappings. Complex Analysis, J. Hersch and A. Huber, eds. Birhhauser, Basel. 225-238. [St] Strebel K, Quadratic Differentials, Springer-Verlag, Berlin, 1984. [Th1] Thurston. W. The geometry and tology of 3-manifolds. Princeton University Notes, 1982. [Th2] Thurston. W. On the geometry and dynamics of diffeomorphisms of surface. Bull. AMS 19. (1988) 417-431 [Th3] Thurston. W. Hyperbolic structures on 3-manifolds II. Surface grups and 3-manifolds that fiber over the circle. Preprint.
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dc.format.extent.spa.fl_str_mv	76 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Medellín - Ciencias - Doctorado en Ciencias - Matemáticas
dc.publisher.department.spa.fl_str_mv	Escuela de matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Medellín
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Medellín
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rodríguez Nieto, José Gregorio4c18915879d90fd92b2c223df2274819Giraldo Galeano, Oscar Iván47f2e778ce962c17adeb92ab7c83752d2021-10-11T16:45:38Z2021-10-11T16:45:38Z2021https://repositorio.unal.edu.co/handle/unal/80486Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustracionesEl objetivo de este trabajo es probar que las laminaciones invariantes bajo un homeomorfismo final periódico f induce una estructura compleja en la superficie. Y para esto, se pasa de laminaciones medibles a foliaciones con singularidades y con medidas transversales. Luego se usa la estructura Euclidiana inducida por las foliaciones para encontrar una estructura conforme. Por último se prueba que f es una función Pseudo Anosov generalizada en el sentido de [deC-H1]. En particular, se prueba que un diferencial cuadrático asociado a las foliaciones tiene área finita. Además se presentan ejemplos particulares del teorema central. (Texto tomado de la fuente)The main result of this paper is to prove that the minimal invariant laminations of an irreducible generalized Pseudo-Anosov homeomorphism isotopic to an endperiodic homeomorphism induces a conformal structure on the singular surface. To have a better understanding of the given theory, three propositions are presented that are original examples, which will give us an idea of the proof of the main theorem.DoctoradoDoctor en Ciencias - Matemáticas76 páginasapplication/pdfspaUniversidad Nacional de ColombiaMedellín - Ciencias - Doctorado en Ciencias - MatemáticasEscuela de matemáticasFacultad de CienciasMedellínUniversidad Nacional de Colombia - Sede Medellín510 - MatemáticasGeometría EuclidianaEuclidean geometryFoliations (mathematics)Foliaciones (MatemáticasSuperficie final periódicaHomeomorfismo final periódicoHomeomorfismo Pseudo-Anosov GeneralizadoEntropía ceroEnd periodic surfacesEnd periodic homeomorphismsGeneralized Pseudo-Anosov homeomorphismsZero entropyHomeomorfismos finales periódicos y Pseudo-Anosov generalizados.End periodic homeomorphisms and generalized pseudo-Anosov homeomorphismsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TD[Ahl] Ahlfors L, Conformal invariants: topics in geometric function theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co. New York (1973) MR0357743[Be-Ha] Bestvida M, Handel M. 1995. Train-Tracks for surfacenhomeomorphisms. Topology Vol. 34. No. I, pp. 109-MO,1995[deC-H1] de Carvalho A, Hall T. 2004. Unimodal generalized pseudo-Anosov maps. Geom Topol 8:1127-1188.[deC2] de Carvalho A. 2005. Extensions, quotients and genelized pseudo-Anosov maps. AMS Proc. Sympos. Pure Math 75:315-338.[deC-P3] de Carvalho A, Patermain M. 2004. Monotone quotients of surface diffeomorphisms. Math. Res. Lett 10:603-619[deC-H4] de Carvalho A, Hall T. 2010. Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences, arXiv:1010.3448.[Fe1] Fenley S. 1990. Endperiodic surface homeomorphisms and 3-manifolds. Math Z. 224:1-24[Fe2] Fenley S. 1992. Asymptotic properties of depth one foliations in hyperbolic 3-manifolds. Jour. Diff. Geo. 36:269-313.[Forster] O. Forster, Riemann Surfaces, Springer-Verlag, 1981.[Ca-Bl] Casson A, Bleiler S. 1988. Automorphisms of surface after Nielsen and Thurston. London Math. Soc. student Text 9 Cambridge Univ. Press.[Ca-Co1] Cantwell J, Conlon L. 2011. Handel-Miller theory and finite depth foliations, arXiv:1006.4525.[Ca-Co2] Cantwell J, Conlon L. 2010. Examples of endperiodic maps, arXiv:1008.2549[Ca-Co3] Cantwell J, Conlon L. 1999. Foliations cones. Geometry and Topology Monographs, Proceedings of the Kirbyfest. 2: 35-86.[Ca-Co4] Cantwell J, Conlon L. 2000. Foliations I. AMS[Ch-Ga-La] Chamanara R, Gardiner F, Lakic N. 2006. A hyperelliptic realization of the horseshoe and baker maps. Ergod. Th. and Dynam. Sys. 26:1749-1768.Fle] Fleming, W. “Nondegenerate surfaces of finite topological type.” Transactions of the American Mathematical Society 90 (1959): 323-335.[Ghys] E. Ghys, Laminations par surfaces de Riemann, Panorames e Synthesis, SMF, 2000.[Ga-La] Gardiner F, Lakic N. 2000. Quasiconformal Teichmuller Theory. AMS. Math. Sur. and Monog. Vol 76.[Ga-Fre] Gardiner F,Frederick P. Measured foliations and the minimal norm property for quadratic differentials. Acta Math., 152(1-2):57-76, 1984.[Gi-Fi] Gilbert H, Ulrich H. Introduction to the geometry of foliations. Part A. Friedr. Vieweg and Sohn, Braunschweig, second edition, 1986. Foliations on compact surfaces, fundamentals for arbitrary codimension, and holonomyGaspard] Gaspard, P. (1998). Chaos, Scattering and Statistical Mechanics (Cambridge Nonlinear Science Series). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511628856[Hu-Ma] Hubbard J, Masur H. 1979. Quadratic differentials and foliations. Acta Math. 142:221-274.[Mi] Sappala M. Foliations and Quadratic Differentials of Riemann Surface.[St] Strebel K. 1988. On the extremality and unique extremality of certain Teichmuller mappings. Complex Analysis, J. Hersch and A. Huber, eds. Birhhauser, Basel. 225-238.[St] Strebel K, Quadratic Differentials, Springer-Verlag, Berlin, 1984.[Th1] Thurston. W. The geometry and tology of 3-manifolds. Princeton University Notes, 1982.[Th2] Thurston. W. On the geometry and dynamics of diffeomorphisms of surface. Bull. AMS 19. (1988) 417-431[Th3] Thurston. W. Hyperbolic structures on 3-manifolds II. Surface grups and 3-manifolds that fiber over the circle. Preprint.InvestigadoresORIGINAL70953160.2021.pdf70953160.2021.pdfTesis de Doctorado en Matemáticas.application/pdf3878839https://repositorio.unal.edu.co/bitstream/unal/80486/4/70953160.2021.pdf7ce5220abe33c79d827bef700eabeb9aMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/80486/3/license.txtcccfe52f796b7c63423298c2d3365fc6MD53THUMBNAIL70953160.2021.pdf.jpg70953160.2021.pdf.jpgGenerated Thumbnailimage/jpeg4261https://repositorio.unal.edu.co/bitstream/unal/80486/5/70953160.2021.pdf.jpgc1f5675a46fb9d9593bb900e4bca3438MD55unal/80486oai:repositorio.unal.edu.co:unal/804862023-07-29 23:03:58.611Repositorio Institucional Universidad Nacional de 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Homeomorfismos finales periódicos y Pseudo-Anosov generalizados.

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