The Extended Monodromy Group and Liouvillian First Integrals

  title={The Extended Monodromy Group and Liouvillian First Integrals},
  author={Henryk Zoladek},
  journal={Journal of Dynamical and Control Systems},
We present a connection between the differential Galois theory and topological Galois theory. The first one is represented by Singer's theorem about integration of polynomial planar vector fields and the second is Khovanskii's monodromy group of a multivalued analytic first integral of such vector field. We show that the monodromy maps together with certain additional maps, which are analogues of the Stokes operators, generate a solvable group.