On the Dynamical Meaning of the Picard–Vessiot Theory

    2001, Volume 6, Number 3, pp.  277-290

    Author(s): Morales-Ruiz J. J., Peris J. M.

    In this paper we present a dynamical interpretation of the Differential Galois Theory of Linear Differential Equations (also called the Picard$ndash;Vessiot Theory). The key point is that when a linear differential equation is not solvable in closed form then by a theorem of Tits the monodromy group for fuchsian equations (or a generalization of it for irregular singularities: the Ramis monodromy group) contains a free non-abelian group. Roughly this free group gives us a very complicated dynamics on some suitable spaces.
    Citation: Morales-Ruiz J. J., Peris J. M., On the Dynamical Meaning of the Picard–Vessiot Theory, Regular and Chaotic Dynamics, 2001, Volume 6, Number 3, pp. 277-290

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