| 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 | |
