On pairs of foliations defined by vector fields in the plane
Jorge Sotomayor Michail Zhitomirskii
Discrete & Continuous Dynamical Systems - A 2000, 6(3): 741-749 doi: 10.3934/dcds.2000.6.741
We obtain a smooth and analytic local classification of pairs of foliations of the plane assuming that one of the foliations is defined by a nonsingular vector field and the other foliation is defined by a singular vector field.
keywords: normal forms vector fields Singular foliation singularities orbital equivalence. local classification
Codimension two umbilic points on surfaces immersed in $R^3$
Jorge Sotomayor Ronaldo Garcia
Discrete & Continuous Dynamical Systems - A 2007, 17(2): 293-308 doi: 10.3934/dcds.2007.17.293
This paper studies the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
keywords: principal curvature lines. umbilic point

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