Análisis espectral de operadores de Schrödinger ergódicos

ilustraciones, fotografías

Autores:: Silva Barbosa, Pablo Blas Tupac

Tipo de recurso:

Fecha de publicación:: 2022

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Análisis espectral de operadores de Schrödinger ergódicos
dc.title.translated.eng.fl_str_mv	Spectral analysis of ergodic Schrödinger operators
title	Análisis espectral de operadores de Schrödinger ergódicos
spellingShingle	Análisis espectral de operadores de Schrödinger ergódicos 510 - Matemáticas Operadores de Schrödinger Espectro continuo Ergodicidad Propiedad de repetición Propiedad de repetición topológica Propiedad de repetición métrica Schrödinger operators Continuous spectrum Ergodicity Repetition property Topological repetition property Metric repetition property
title_short	Análisis espectral de operadores de Schrödinger ergódicos
title_full	Análisis espectral de operadores de Schrödinger ergódicos
title_fullStr	Análisis espectral de operadores de Schrödinger ergódicos
title_full_unstemmed	Análisis espectral de operadores de Schrödinger ergódicos
title_sort	Análisis espectral de operadores de Schrödinger ergódicos
dc.creator.fl_str_mv	Silva Barbosa, Pablo Blas Tupac
dc.contributor.advisor.none.fl_str_mv	Álvarez Bilbao, Rafael José Bautista Díaz, Serafín
dc.contributor.author.none.fl_str_mv	Silva Barbosa, Pablo Blas Tupac
dc.contributor.researchgroup.spa.fl_str_mv	Sisdimunal
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas
topic	510 - Matemáticas Operadores de Schrödinger Espectro continuo Ergodicidad Propiedad de repetición Propiedad de repetición topológica Propiedad de repetición métrica Schrödinger operators Continuous spectrum Ergodicity Repetition property Topological repetition property Metric repetition property
dc.subject.proposal.spa.fl_str_mv	Operadores de Schrödinger Espectro continuo Ergodicidad Propiedad de repetición Propiedad de repetición topológica Propiedad de repetición métrica
dc.subject.proposal.eng.fl_str_mv	Schrödinger operators Continuous spectrum Ergodicity Repetition property Topological repetition property Metric repetition property
description	ilustraciones, fotografías
publishDate	2022
dc.date.accessioned.none.fl_str_mv	2022-10-11T06:05:40Z
dc.date.available.none.fl_str_mv	2022-10-11T06:05:40Z
dc.date.issued.none.fl_str_mv	2022-10-07
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
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dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional 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.indexed.spa.fl_str_mv	RedCol LaReferencia
dc.relation.references.spa.fl_str_mv	Avila, A. and Damanik, D. (2005). Generic singular spectrum for ergodic schrödinger ope rators. Duke Mathematical Journal, 130:393–400. Axler, S. (2015). Linear Algebra Done Right. Springer-Verlag, New York Axler, S. (2020). Measure, Integration Real Analysis. Springer-Verlag, New York. Boshernitzan, M. and Damanik, D. (2008). Generic continuous spectrum for ergodic schrö dinger operators. Communications in Mathematical Physics, 283:647–662. Brom, J. (1977). The theory of almost periodic functions in constructive mathematics. Pacific Journal of Mathematics, 70:67–81 Catsigeras, E. (2013). Teoría Ergódica. De los Atractores Topológicos y Estadísticos. Instituto Venezolano de Investigaciones Científicas, Caracas, Venezuela. Cornfeld, I., Fomin, S., and Sinái, Y. (1982). Ergodic Theory. Springer-Verlag, New York. Cycon, H., Froese, R., Kirsch, W., and Simon, B. (1987). Schrödinger Operators with Appli cations to Quantum Mechanics and Global Geometry. Springer-Verlag, Germany. Damanik, D. (2017). Schrödinger operators with dynamically defined potentials. Electronic Journal of Differential Equations, 37:1681–1764. Damanik, D. and Stolz, G. (2000). A generalization of gordon’s theorem and applications to quasiperiodic schrödinger operators. Electronic Journal of Differential Equations, 55:1–8. Fan, Y. and Han, R. (2018). Generic continuous spectrum for multi-dimensional quasiperio dic schrödinger operators with rough potentials. Journal of Spectral Theory, 8:1635–1645. Huang, W., Xu, L., and Yi, Y. (2010). Entropy of dynamical systems with repetition property. Journal of Dynamics and Differential Equations, 23:683–693. Jitomirskaya, S. (2007). Ergodic schrödinger operators (on one foot). Proceeings of Symposia in Pure Mathematical, 76:613–647. Khinchin, A. Y. (1964). Continued Fractions. The University of Chicago Press, Chicago Kirsch, W. (2007). An Invitation to Random Schrödinger Operators. Institut für Mathematik Ruhr-Universität Bochum, Bochum. Kohlman, M. (2018). Schrödinger Operators and their Spectra. Georg-August-Universität, Göttingen. Kreyszig, E. (1978). Introductory Functional Analysis with Applications. John Wiley and Sons, Canada Lenz, D. (2002). Singular spectrum of lebesgue measure zero for one-dimensional quasicrys tals. Communications in Mathematical Physics, 227:119–120. Moreira, J. (2020). Ergodic Theory. University of Warwick, United Kingdom Oxtoby, J. (1980). Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces. Springer-Verlag, New York. Reed, M. and Simon, B. (1980). Methods of modern mathematical physics. Academic Press, Inc., San Diego. Renn, J. (2013). Schrödinger and the Genesis of Wave Mechanics. Max Planck Institute for the History of Science, Berlin. Simon, B. (1982). Almost periodic schrödinger operators: A review. Advances in Applied Mathematics, 3:463–490. Simon, B. (2000). Schrödinger operators in the twentieth century. Journal of Mathematical Physics, 41:3523–3555 Spitzer, F. (1976). Principles of Random Walk. Springer-Verlag, New York Viana, M. and Oliveira, K. (2016). Foundations of Ergodic Theory. Cambridge University Press, Cambridge. Walters, P. (1982). An Introduction to Ergodic Theory. Springer-Verlag, New York Zhecheva, I. (2008). Ergodic Properties of Random Schrödinger Operators. Williams College, Massachusetts
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dc.format.extent.spa.fl_str_mv	x, 72 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Maestría en Ciencias - Matemáticas
dc.publisher.department.spa.fl_str_mv	Departamento de Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Álvarez Bilbao, Rafael José4940d54edae52124abf3a9db501da276Bautista Díaz, Serafína108a3a090f66f796c78ca0fa2c7e363Silva Barbosa, Pablo Blas Tupac66932b07cc1eb8cceec5fef66aa3680eSisdimunal2022-10-11T06:05:40Z2022-10-11T06:05:40Z2022-10-07https://repositorio.unal.edu.co/handle/unal/82361Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, fotografíasEn este trabajo final de maestría estudiamos los tipos espectrales de las familias de operadores de Schrödinger unidimensionales discretos {Hω}ω∈Ω en las que el potencial de Hω está dado por Vω(n) = f(T nω), para n ∈ Z, donde f : Ω → R es una función continua y T es un homeomorfismo ergódico en un espacio compacto Ω. Con base en la investigación de Boshernitzan y Damanik (2008), definimos las propiedades de repetición topológica y métrica en el sistema dinámico {Ω, T} y demostramos detalladamente que cada una de estas propiedades es condición suficiente para que el espectro puramente continuo sea una propiedad genérica de {Hω}ω∈Ω. La principal herramienta del trabajo es el lema de Gordon, del cual propone mos una demostración paso a paso y analizamos sus implicaciones. También exponemos y demostramos dos resultados propios que generalizan el teorema central de la investigación. citada y discutimos ejemplos de aplicación. (Texto tomado de la fuente)In this thesis we study the spectral types of the families of discrete one-dimensional Schrödinger operators {Hω}ω∈Ω in which the potential of Hω is given by Vω(n) = f(T nω), for n ∈ Z, where f : Ω → R is a continuous function and T is an ergodic homeomorphism on a compact space Ω. Based on the research of Boshernitzan and Damanik (2008), we define the topological and metric repetition properties on the dynamical system {Ω, T} and show that each of these properties is a sufficient condition for the purely continuous spectrum to be a generic property of {Hω}ω∈Ω. The main tool of the work is Gordon’s lemma, of which we propose a step-by-step demonstration and analyze its implications. We propose two ge neralizations of the main theorem of the above research and discuss examples of application.MaestríaSistemas dinámicosx, 72 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - MatemáticasOperadores de SchrödingerEspectro continuoErgodicidadPropiedad de repeticiónPropiedad de repetición topológicaPropiedad de repetición métricaSchrödinger operatorsContinuous spectrumErgodicityRepetition propertyTopological repetition propertyMetric repetition propertyAnálisis espectral de operadores de Schrödinger ergódicosSpectral analysis of ergodic Schrödinger operatorsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMRedColLaReferenciaAvila, A. and Damanik, D. (2005). Generic singular spectrum for ergodic schrödinger ope rators. Duke Mathematical Journal, 130:393–400.Axler, S. (2015). Linear Algebra Done Right. Springer-Verlag, New YorkAxler, S. (2020). Measure, Integration Real Analysis. Springer-Verlag, New York.Boshernitzan, M. and Damanik, D. (2008). Generic continuous spectrum for ergodic schrö dinger operators. Communications in Mathematical Physics, 283:647–662.Brom, J. (1977). The theory of almost periodic functions in constructive mathematics. Pacific Journal of Mathematics, 70:67–81Catsigeras, E. (2013). Teoría Ergódica. De los Atractores Topológicos y Estadísticos. Instituto Venezolano de Investigaciones Científicas, Caracas, Venezuela.Cornfeld, I., Fomin, S., and Sinái, Y. (1982). Ergodic Theory. Springer-Verlag, New York.Cycon, H., Froese, R., Kirsch, W., and Simon, B. (1987). Schrödinger Operators with Appli cations to Quantum Mechanics and Global Geometry. Springer-Verlag, Germany.Damanik, D. (2017). Schrödinger operators with dynamically defined potentials. Electronic Journal of Differential Equations, 37:1681–1764.Damanik, D. and Stolz, G. (2000). A generalization of gordon’s theorem and applications to quasiperiodic schrödinger operators. Electronic Journal of Differential Equations, 55:1–8.Fan, Y. and Han, R. (2018). Generic continuous spectrum for multi-dimensional quasiperio dic schrödinger operators with rough potentials. Journal of Spectral Theory, 8:1635–1645.Huang, W., Xu, L., and Yi, Y. (2010). Entropy of dynamical systems with repetition property. Journal of Dynamics and Differential Equations, 23:683–693.Jitomirskaya, S. (2007). Ergodic schrödinger operators (on one foot). Proceeings of Symposia in Pure Mathematical, 76:613–647.Khinchin, A. Y. (1964). Continued Fractions. The University of Chicago Press, ChicagoKirsch, W. (2007). An Invitation to Random Schrödinger Operators. Institut für Mathematik Ruhr-Universität Bochum, Bochum.Kohlman, M. (2018). Schrödinger Operators and their Spectra. Georg-August-Universität, Göttingen.Kreyszig, E. (1978). Introductory Functional Analysis with Applications. John Wiley and Sons, CanadaLenz, D. (2002). Singular spectrum of lebesgue measure zero for one-dimensional quasicrys tals. Communications in Mathematical Physics, 227:119–120.Moreira, J. (2020). Ergodic Theory. University of Warwick, United KingdomOxtoby, J. (1980). Measure and Category. A Survey of the Analogies Between Topological and Measure Spaces. Springer-Verlag, New York.Reed, M. and Simon, B. (1980). Methods of modern mathematical physics. Academic Press, Inc., San Diego.Renn, J. (2013). Schrödinger and the Genesis of Wave Mechanics. Max Planck Institute for the History of Science, Berlin.Simon, B. (1982). Almost periodic schrödinger operators: A review. Advances in Applied Mathematics, 3:463–490.Simon, B. (2000). Schrödinger operators in the twentieth century. Journal of Mathematical Physics, 41:3523–3555Spitzer, F. (1976). Principles of Random Walk. Springer-Verlag, New YorkViana, M. and Oliveira, K. (2016). Foundations of Ergodic Theory. Cambridge University Press, Cambridge.Walters, P. (1982). An Introduction to Ergodic Theory. Springer-Verlag, New YorkZhecheva, I. (2008). Ergodic Properties of Random Schrödinger Operators. Williams College, MassachusettsEstudiantesInvestigadoresPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/82361/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53ORIGINALTesisPabloSilva.pdfTesisPabloSilva.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf1500902https://repositorio.unal.edu.co/bitstream/unal/82361/4/TesisPabloSilva.pdf827747b017d514a063711b71ad724faaMD54THUMBNAILTesisPabloSilva.pdf.jpgTesisPabloSilva.pdf.jpgGenerated Thumbnailimage/jpeg4211https://repositorio.unal.edu.co/bitstream/unal/82361/5/TesisPabloSilva.pdf.jpgb6734f0623518ee573e2c36a0af93776MD55unal/82361oai:repositorio.unal.edu.co:unal/823612023-08-09 23:04:33.321Repositorio Institucional Universidad Nacional de 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Análisis espectral de operadores de Schrödinger ergódicos

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