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On the Dynamical Meaning of Picard-Vessiot David Blazquez-Sanz

Summary: On the Dynamical Meaning of Picard-Vessiot
David Bl´azquez-Sanz
The aim of these notes is to introduce the classical Picard-Vessiot from
the standpoint of complex geometry. These notes were written as mate-
rials for a lecture entitled "On the dynamical meaning of Picard-Vessiot
theory" given in the Kyoto Dynamic Days 9 at Kyoto University and
the first part of a lecture entitled "Liouville invariant tori of completely
integrable linear Hamiltonian systems from the standpoint of differential
Galois theory" at Kanazawa University. These notes only cover the core
of the theory and the problem of integration by quadratures. Therefore so
many interesting applications and related topics could be added to cover
the ambitious title. The author hopes these notes are suitable for under-
graduate students with some knowledge on Riemann surfaces, homotopy,
analytic functions and group theory.
1 Introduction 2
2 Monodromy Representation 7
3 Univalued Solutions 10


Source: Arai, Zin - Department of Mathematics, Kyoto University


Collections: Mathematics