On Hamiltonian potentials with cuartic polynomial normal variational equations

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/2234

Title:	On Hamiltonian potentials with cuartic polynomial normal variational equations
Author:	Acosta Humánez, Primitivo Belén; Blázquez Sanz, David; Vargas Contreras, Camilo
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	Here we find the complete family of two degree of freedom classical Hamiltonians with invariant plane $\Gamma=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $\Gamma$ is a generically a Hill-Schr\"odinger equation with cuartic polynomial potential. In particular, these Hamiltonian form a family of non-integrable Hamiltonians through rational first integrals.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Hamiltonian systems -Differential algebra -Difference algebra -Hamiltonian dynamical systems -Lagrangian functions -Morales-Ramis theory -Hamiltonian system -non-integrability -normal variational equation -Hamilton, Sistemes de -Àlgebra diferencial -Lagrange, Funcions de -Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -Classificació AMS::12 Field theory and polynomials::12H Differential and difference algebra -Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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