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dc.contributor.authorAcosta Humánez, Primitivo Belén
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.description.abstractIn this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with $1+1/2$ degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlevé II, Sitnikov and Hill-Schrödinger equation. We emphasize in Painlevé II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.
dc.format.extent18 p.
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential algebra
dc.subject.lcshHamiltonian systems
dc.subject.otherHill-Schrödinger equation
dc.subject.othervirtually abelian groups
dc.subject.otherMorales-Ramis theory
dc.subject.othernon-autonomous Hamiltonian systems
dc.subject.othernon-integrability of Hamiltonian systems
dc.subject.otherPainlevé II equation
dc.subject.otherSitnikov problem
dc.titleNon-autonomous hamiltonian systems and Morales-Ramis theory
dc.subject.lemacÀlgebra diferencial
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacHamiltonian dynamical systems
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::12 Field theory and polynomials::12H Differential and difference algebra
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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