5 citations · 9 across the 9 of their papers we have counts for
9 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…
Abelian integrals for polynomials with trivial global monodromy on
Jesús Muciño-Raymundo, Salomón Rebollo-Perdomo
We consider infinitesimal perturbations of Hamiltonian differential equations on the complex plane , where is a polynomial of degree …
Plane polynomials and Hamiltonian vector fields determined by their singular points
John A. Arredondo, Jesús Muciño-Raymundo
Let be critical points of a polynomial in the plane , where is or . Our goal is to study the crit…
Integrability and adapted complex structures to smooth vector fields on the plane
Gaspar León-Gil, Jesús Muciño-Raymundo
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We descri…
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 ${\mathscr E}(r,d)=\left\{ X(z)=\frac{1}{P(z)} e^{E(z)}\frac{\…
Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
Alvaro Alvarez-Parrilla, Jesús Muciño-Raymundo
We consider the family with polynomials, deg, deg and deg$(…
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…