Non-integrability of some Hamiltonians with rational potentials

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dc.creatorAcosta-Humanez, Primitivo
dc.creatorBlazquez-Sanz, David
dc.date2006-10-06
dc.date.accessioned2026-07-07T07:28:26Z
dc.date.available2026-07-07T07:28:26Z
dc.descriptionIn this work we compute the families of classical Hamiltonians in two degrees of freedom in which the Normal Variational Equation around an invariant plane falls in Schroedinger type with polynomial or trigonometrical potential. We analyze the integrability of Normal Variational Equation in Liouvillian sense using the Kovacic's algorithm. We compute all Galois groups of Schroedinger type equations with polynomial potential. We also introduce a method of algebrization that transforms equations with transcendental coefficients in equations with rational coefficients without changing essentially the Galoisian structure of the equation. We obtain Galoisian obstructions to existence of a rational first integral of the original Hamiltonian via Morales-Ramis theory.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0610010
dc.identifierhttp://arxiv.org/abs/math-ph/0610010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117735
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subject37J30; 34M15
dc.titleNon-integrability of some Hamiltonians with rational potentials
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