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dc.contributor.authorAcosta Humánez, Primitivo Belén
dc.contributor.authorBlázquez Sanz, David
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.identifier.citationAcosta-Humanez, P.; Blazquez-Sanz, D. Non-integrability of some hamiltonians with rational potentials. Discrete and Continuous Dynamical Systems Series B, 2008, vol. 10, p. 265-293.
dc.description.abstractIn this paper we give a mechanism to compute the families of classical hamiltonians of two degrees of freedom with an invariant plane and normal variational equations of Hill-Schr\"odinger type selected in a suitable way. In particular we deeply study the case of these equations with polynomial or trigonometrical potentials, analyzing their integrability in the Picard-Vessiot sense using Kovacic's algorithm and introducing an algebraic method (algebrization) that transforms equations with transcendental coefficients in equations with rational coefficients without changing the Galoisian structure of the equation. We compute all Galois groups of Hill-Schr\"odinger type equations with polynomial and trigonometric (Mathieu equation) potentials, obtaining Galoisian obstructions to integrability of hamiltonian systems by means of meromorphic or rational first integrals via Morales-Ramis theory.
dc.format.extent29 p.
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshHamiltonian systems
dc.subject.lcshDifferential algebra
dc.subject.lcshDifference algebra
dc.subject.lcshHamiltonian dynamical systems
dc.subject.lcshLagrangian functions
dc.subject.otherAlgebrization algorithm
dc.subject.otherAutonomous Hamiltonian systems
dc.subject.otherHill-Schrödinger equation
dc.subject.otherKovacic algorithm
dc.subject.otherMorales-Ramis theory
dc.subject.otherNon-integrability of Hamiltonian systems
dc.subject.otherVirtually abelian groups
dc.titleNon-integrability of some hamiltonians with rational potentials
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacÀlgebra diferencial
dc.subject.lemacHamilton, Sistemes de
dc.subject.lemacLagrange, Funcions de
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::12 Field theory and polynomials::12H Differential and difference algebra
dc.subject.amsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
dc.rights.accessOpen Access

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