On the geometry, flows and visualization of singular complex analytic vector fields on Riemann surfaces
Alvaro Alvarez-Parrilla,
Jesús Muciño-Raymundo,
Selene Solorza-Calderón
et al.
Abstract:Motivated by the wild behavior of isolated essential singularities in complex analysis, we study singular complex analytic vector fields X on arbitrary Riemann surfaces M . By vector field singularities we understand zeros, poles, isolated essential singularities and accumulation points of the above kind. In this framework, a singular analytic vector field X has canonically associated; a 1-form, a quadratic differential, a flat metric (with a geodesic foliation), a global distinguished parameter or C-flow box … Show more
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