Some tastings in Morales-Ramis Theory
Primitivo Bel\'en Acosta-Hum\'anez, Germ\'an Jim\'enez Blanco
TL;DR
This paper explores Morales-Ramis theory, linking Hamiltonian system integrability with differential Galois theory, and computes the abelian differential Galois group for a specific bi-parametric Hamiltonian system.
Contribution
It provides the first computation of the abelian differential Galois group for the variational equation of a bi-parametric Hamiltonian system.
Findings
Determined the abelian differential Galois group for the variational equation.
Connected integrability notions in Hamiltonian and differential equations.
Enhanced understanding of Morales-Ramis theory applications.
Abstract
In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian Systems through Liouville Arnold Theorem and Integrability of Linear Differential Equations through Differential Galois Theory. As contribution, we obtain the abelian differential Galois group of the variational equation related to a bi-parametric Hamiltonian system,
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