View Item 
        •   Utrecht University Student Theses Repository Home
        • UU Theses Repository
        • Theses
        • View Item
        •   Utrecht University Student Theses Repository Home
        • UU Theses Repository
        • Theses
        • View Item
        JavaScript is disabled for your browser. Some features of this site may not work without it.

        Browse

        All of UU Student Theses RepositoryBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

        Existence of Riemann surfaces through an equilibrium of a tangent holomorphic vector field

        Thumbnail
        View/Open
        master_thesis.pdf (626.8Kb)
        Publication date
        2022
        Author
        Huiszoon, Constant
        Metadata
        Show full item record
        Summary
        It is shown that every holomorphic vector field that vanishes at a point where its derivative is invertible has a Riemann surface such that the vector field is tangent to the Riemann surface and such that the Riemann surface contains the point. In fact, we give a precise finite lower bound on the number of (germs of) such Riemann surfaces depending on the derivative of the vector field at such a point. We use for this a differentiable version of the Grobman-Hartman theorem. Additionally, we conjecture an upper bound on the number of independent integrals a vector field may have near an equilibrium. In the presentation, a newly developed notional system is used.
        URI
        https://studenttheses.uu.nl/handle/20.500.12932/43308
        Collections
        • Theses
        Utrecht university logo