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oai:recercat.cat:2099.1/231132025-07-23T06:34:33Zcom_2072_1033col_2072_452951

How to apply numerical tools to study dynamical systems : The CP problem Aranda May, Montserrat Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I Ollé Torner, Mercè Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Numerical analysis Numerical Methods Dynamical Systems Hamiltonian Systems Anàlisi numèrica Classificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systems Given a system of differential equations, normally it is not possible to find the associated solutions analytically, so other ways have to be taken into account in order to describe the behaviour of the system. The goal of this thesis is to study how to construct numerically the skeleton of a given dynamical system, starting with the computation of the easiest solutions -equilibrium points- and following with other invariant objects as manifolds of equilibria, homoclinic orbits, periodic orbits (PO), manifolds of PO, chaos, island chains, etc. Thanks to these particular solutions and using well-known theory of Dynamical Systems, one can get an idea of the general behaviour of the system. The project studies the particular case of the system that models the behaviour of a hydrogen atom in a circularly polarized microwave field (CP problem). 2014-07 Master thesis https://hdl.handle.net/2099.1/23113 FME-1000 eng Open Access application/pdf Universitat Politècnica de Catalunya