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Computer-Assited Proofs in Dynamics
dc.contributor | Puig Sadurní, Joaquim |
dc.contributor.author | Fernández Pinto, Aarón |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2020-11-20T14:26:17Z |
dc.date.issued | 2020-10 |
dc.identifier.uri | http://hdl.handle.net/2117/332728 |
dc.description.abstract | Interval 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.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
dc.subject.lcsh | Differentiable dynamical systems |
dc.subject.other | Interval analysis |
dc.subject.other | Real analysis |
dc.subject.other | Computer-assisted proof |
dc.subject.other | Dynamical systems |
dc.subject.other | Hill equation |
dc.subject.other | Mathieu equation |
dc.subject.other | C++. |
dc.title | Computer-Assited Proofs in Dynamics |
dc.type | Master thesis |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems |
dc.identifier.slug | FME-1872 |
dc.rights.access | Restricted access - author's decision |
dc.date.lift | 10000-01-01 |
dc.date.updated | 2020-10-23T05:28:57Z |
dc.audience.educationlevel | Màster |
dc.audience.mediator | Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
dc.audience.degree | MÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010) |