Master Thesis

My master thesis concerns first order Painlevé equations and was carried out under the supervision of Marius van der Put, Jaap Top and Boele Braaksma.


  • Master Thesis: The Classification of the First Order Ordinary Differential Equations with the Painlevé Property (PDF)

  • Master Thesis Paper: G. Muntingh, M. van der Put. Order One Equations with the Painlevé Property. Indagationes Mathematicae, N.S., 18 (1), 2007, Pages 83 – 95. (pre-print PDF)

    • Abstract: Differential equations with the Painlevé property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order one equations appeared before, the connection with the classical theory did not. Using techniques from algebraic geometry we provide the link between the classical and the modern treatment, and with the help of differential Galois theory a new classification is derived, both for characteristic 0 and p.

  • Master Thesis Presentation: The First Order Ordinary Differential Equations with the Painlevé property (PDF)

      • Abstract: Differential equations with the Painlevé property play a special role in physics. They have been studied extensively, and have connections to many branches of mathematics, including function theory, dynamical systems and differential algebraic geometry. In some sense, one can say that they form a class broad enough to capture many phenomena, but on the other hand narrow enough to be able to say sensible things about them. Assuming only some mathematics taught in high school, we shall start with elucidating the concept of a differential equation, followed by an explanation of what it means for a differential equation to have the Painlevé property. After this, we will consider in a conceptual way first order ordinary differential equations from two points of view: the classical function theoretic approach, and a modern differential algebraic geometric approach. Historical details will be given, and the talk ends with a classification theorem.