Differentiable equisingularity of holomorphic foliations
Copyright policy )Differentiable equisingularity of holomorphic foliations
We prove that a $C^{\infty}$ equivalence between germs holomorphic foliations at $({\mathbb C}^2,0)$ establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.
invariant curves, Singularities of holomorphic vector fields and foliations, holomorphic foliations, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, equidesingularization, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, vector fields, 32S65
invariant curves, Singularities of holomorphic vector fields and foliations, holomorphic foliations, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, equidesingularization, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, vector fields, 32S65
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