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math.DS2025
Fake saddles and their transition maps
David MarÃn
We study degenerate singular points of planar vector fields inside a (degenerated) flow-box. These kind of singularities are called fake saddles and their linear parts are always z…
math.DS2025
The cyclicity of hyperbolic hemicycles
David MarÃn, Jordi Villadelprat
We consider families of planar polynomial vector fields of degree and study the cyclicity of a type of unbounded polycycle~ called hemicycle. Compactified to the Poincaré…
math.DS2024
Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families
David MarÃn, Jean-François Mattei, Eliane Salem
In this work we use our previous results on the topological classification of generic singular foliation germs on to construct complete families: after fixing t…