Characterization of second type plane foliations using Newton polygons

Fernández-Sánchez P.; García Barroso E.R.; Saravia-Molina N. · Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica (2022) · DOI: 10.2478/auom-2022-0021

Resumen

In this article we characterize the foliations that have the same Newton polygon that their union of formal separatrices, they are the foliations called of the second type. In the case of cuspidal foliations studied by Loray [Lo], we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same process of singularity reduction that the union of its separatrices. Finally we give necessary and sufficient conditions when these cuspidal foliations are generalized curves, and a characterization when they have only one separatrix.

Instituciones: Pontificia Universidad Católica del Perú