TY - JOUR
T1 - Characterization of second type plane foliations using Newton polygons
AU - Fernández-Sánchez, Percy
AU - Saravia, Nancy
AU - García Barroso, Evelia R.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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, we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same desingularization 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.
AB - 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, we precise this characterization using the Poincaré-Hopf index. This index also characterizes the cuspidal foliations having the same desingularization 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.
UR - https://arxiv.org/abs/1812.06530
M3 - Artículo
SN - 1224-1784
VL - 30
SP - 103
EP - 123
JO - Analele Stiintifice ale Universitatii Ovidius Constanta
JF - Analele Stiintifice ale Universitatii Ovidius Constanta
IS - 2
ER -