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math.CV2023
Complexity of Puiseux solutions of differential and -difference equations of order and degree one
José Cano Torres, Pedro Fortuny Ayuso, Javier Ribón
We relate the complexity of both differential and -difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are c…
math.CV2023
The Poincaré problem for reducible curves
Pedro Fortuny Ayuso, Javier Ribón
We provide sharp lower bounds for the multiplicity of a local holomorphic foliation defined in a complex surface in terms of data associated to a germ of invariant curve. Then we a…
math.DS2023
Nondegenerate germs of holomorphic foliations with prescribed holonomy
Javier Ribón, Rudy Rosas
We are interested in characterizing the holonomy maps associated to integral curves of non-degenerate singularities of holomorphic vector fields. Such a description is well-known i…