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dc.contributorPuig Sadurní, Joaquim
dc.contributor.authorFernández Pinto, Aarón
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2020-11-20T14:26:17Z
dc.date.issued2020-10
dc.identifier.urihttp://hdl.handle.net/2117/332728
dc.description.abstractInterval analysis is presented as a solution to obtain rigorous results using computers. We present a methodology of computer-assisted proofs which involves the use of interval computations. In this thesis we introduce the main concepts of interval analysis, as well as how some different calculations and methods are adapted to it. We present the CAPD::DynSys C++ library for rigorous computation. We present different proofs in the analysis of some types of Hill's equations, such as the existence of an instability pocket for a perturbation of the classical case of the Mathieu equation, analyze the behaviour of the pocket under other perturbation and enclose some interesting results from combinations of parameters for a particular case of the Mathieu equation. For all these calculations, we develop the appropriate C++ using the CAPD::DynSys libraries.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshDifferentiable dynamical systems
dc.subject.otherInterval analysis
dc.subject.otherReal analysis
dc.subject.otherComputer-assisted proof
dc.subject.otherDynamical systems
dc.subject.otherHill equation
dc.subject.otherMathieu equation
dc.subject.otherC++.
dc.titleComputer-Assited Proofs in Dynamics
dc.typeMaster thesis
dc.subject.lemacSistemes dinàmics diferenciables
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
dc.identifier.slugFME-1872
dc.rights.accessRestricted access - author's decision
dc.date.lift10000-01-01
dc.date.updated2020-10-23T05:28:57Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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