5 citations · 11 across the 7 of their papers we have counts for
7 papers
Tessellations and Speiser graphs arising from meromorphic functions on simply connected Riemann surfaces
Alvaro Alvarez-Parrilla, Jesus Muciño-Raymundo
Motivated by W. P. Thurston, we ask: What is the shape of a meromorphic function on a simply connected Riemann surface ? We consider Speiser functions, i.e. meromorphic functi…
Tessellations of rational complex functions and the Riemann's existence theorem
Alvaro Alvarez-Parrilla, Roberto Gutiérrez-Soto, Jesús Muciño-Raymundo
A complex rational function R, of degree n>1, on a compact Riemann surface M provided with a cyclic order of its q critical values, determines an homogeneous tessellation of the Ri…
Geometry of transcendental singularities of complex analytic functions and vector fields
Alvaro Alvarez-Parrilla, Jesús Muciño-Raymundo
On Riemann surfaces , there exists a canonical correspondence between a possibly multivalued function whose differential is single valued ( an additively automorphic…
Dynamics of singular complex analytic vector fields with essential singularities II
Alvaro Alvarez-Parrilla, Jesús Muciño-Raymundo
The singular complex analytic vector fields on the Riemann sphere belonging to the family ${\mathscr E}(r,d)=\left\{ X(z)=\frac{1}{P(z)} e^{E(z)}\frac{\…
Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
Alvaro Alvarez-Parrilla, Jesús Muciño-Raymundo
We consider the family with polynomials, deg, deg and deg$(…
Classification of rational differential forms on the Riemann sphere, via their isotropy group
Alvaro Alvarez-Parrilla, Martín Eduardo Frías-Armenta, Carlos Yee-Romero
We classify the rational differential 1-forms with simple poles and simple zeros on the Riemann sphere according to their isotropy group; when the 1-form has exactly two poles the…
On the geometry, flows and visualization of singular complex analytic vector fields on Riemann surfaces
Alvaro Alvarez-Parrilla, Jesús Muciño-Raymundo, Selene Solorza-Calderón +1
Motivated by the wild behavior of isolated essential singularities in complex analysis, we study singular complex analytic vector fields on arbitrary Riemann surfaces . By v…