dc.rights.license CC-BY-NC-ND dc.contributor.advisor Hanssmann, Heinz dc.contributor.author Huiszoon, Constant dc.date.accessioned 2022-12-10T00:00:36Z dc.date.available 2022-12-10T00:00:36Z dc.date.issued 2022 dc.identifier.uri https://studenttheses.uu.nl/handle/20.500.12932/43308 dc.description.abstract 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. dc.description.sponsorship Utrecht University dc.language.iso EN dc.subject 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. Additionally, a an upper bound on the number of independent integrals a vector field may have near an equilibrium is conjectured. In the presentation, a newly developed notional system is used. dc.title Existence of Riemann surfaces through an equilibrium of a tangent holomorphic vector field dc.type.content Master Thesis dc.rights.accessrights Open Access dc.subject.keywords holomorphic vector field; equilibrium; singularity; invariant Riemann surface; notation; non-integrability; Grobman-Hartman theorem; Hartman-Grobman theorem dc.subject.courseuu Mathematical Sciences dc.thesis.id 12545
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