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Lyapunov Exponents to Predict the Behavior of the Product of Random Matrices

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dc.contributor.advisorArtigiani, Mauro
dc.contributor.advisorMartínez, Cristian
dc.creatorBermúdez Guzmán, Juliana
dc.creator.degreeProfesional en Matemáticas Aplicadas y Ciencias de la Computación
dc.creator.degreeProfesional en Matemáticas Aplicadas y Ciencias de la Computación
dc.creator.degreeLevelPregrado
dc.date.accessioned2025-06-19T14:33:07Z
dc.date.available2025-06-19T14:33:07Z
dc.date.created2025-06-09
dc.descriptionIn this thesis, we investigate the asymptotic behavior of products of random matrices through Lyapunov exponents. Our theoretical framework is grounded in Kingman’s Subadditive Ergodic Theorem, from which we derive the Furstenberg-Kesten Theorem and Oseledets’ Theorem in two dimensions. These results provide the tools to quantify exponential growth rates and directional behavior in random matrix products. To visualize our theoretical conclusions, we present a series of simulations that illustrate the emergence of Lyapunov exponents and their predictive power in practical settings.
dc.description.abstractIn this thesis, we investigate the asymptotic behavior of products of random matrices through Lyapunov exponents. Our theoretical framework is grounded in Kingman’s Subadditive Ergodic Theorem, from which we derive the Furstenberg-Kesten Theorem and Oseledets’ Theorem in two dimensions. These results provide the tools to quantify exponential growth rates and directional behavior in random matrix products. To visualize our theoretical conclusions, we present a series of simulations that illustrate the emergence of Lyapunov exponents and their predictive power in practical settings.
dc.format.extent40 pp
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.48713/10336_45741
dc.identifier.urihttps://repository.urosario.edu.co/handle/10336/45741
dc.language.isoeng
dc.publisherUniversidad del Rosario
dc.publisher.departmentEscuela de Ingeniería, Ciencia y Tecnología
dc.publisher.programPrograma de Matemáticas Aplicadas y Ciencias de la Computación - MACC
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.accesRightsinfo:eu-repo/semantics/openAccess
dc.rights.accesoAbierto (Texto Completo)
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
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dc.source.instnameinstname:Universidad del Rosario
dc.source.reponamereponame:Repositorio Institucional EdocUR
dc.subjectExponentes de Lyapunov
dc.subjectMatrices aleatorios
dc.subjectCaos
dc.subjectTeoría ergódica
dc.subject.keywordLyapunov Exponents
dc.subject.keywordRandom Matrices
dc.subject.keywordChaos
dc.subject.keywordErgodic Theory
dc.titleLyapunov Exponents to Predict the Behavior of the Product of Random Matrices
dc.title.TranslatedTitleExponentes de Lyapunov para predecir el comportamiento del producto de matrices aleatorias
dc.typebachelorThesis
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersion
dc.type.spaTrabajo de grado
local.department.reportEscuela de Ingeniería, Ciencia y Tecnología
local.regionesBogotá
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