Non-integrability of some hamiltonians with rational potentials
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hdl:2117/2236
Tipus de documentArticle
Data publicació2008-09-01
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
In 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.
CitacióAcosta-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.
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