Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case $ddot{x}=fx,t$ - Mathematical PhysicsReport as inadecuate




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Abstract: In this paper we present an approach towards the comprehensive analysis ofthe non-integrability of differential equations in the form $\ddot x=fx,t$which is analogous to Hamiltonian systems with 1+1-2 degree of freedom. Inparticular, we analyze the non-integrability of some important families ofdifferential equations such as Painlev\-e II, Sitnikov and Hill-Schr\-odingerequation.We emphasize in Painlev\-e II, showing its non-integrability through threedifferent Hamiltonian systems, and also in Sitnikov in which two differentversion including numerical results are shown. The main tool to study thenon-integrability of these kind of Hamiltonian systems is Morales-Ramis theory.This paper is a very slight improvement of the talk with the almost-same titledelivered by the author in SIAM Conference on Applications of Dynamical Systems2007.



Author: Primitivo B. Acosta-Humanez

Source: https://arxiv.org/







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