 
Summary: On the Dynamical Meaning of PicardVessiot
Theory
David Bl´azquezSanz
Abstract
The aim of these notes is to introduce the classical PicardVessiot from
the standpoint of complex geometry. These notes were written as mate
rials for a lecture entitled "On the dynamical meaning of PicardVessiot
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.
Contents
1 Introduction 2
2 Monodromy Representation 7
3 Univalued Solutions 10
