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Fake saddles and their transition maps
David Marín
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…
The cyclicity of hyperbolic hemicycles
David Marín, 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 di…
The period of the limit cycle bifurcating from a persistent polycycle
David Marín, Lucas Queiroz, Jordi Villadelprat
We consider smooth families of planar polynomial vector fields , where is an open subset of , for which there is a hyperbolic polycycle that…
Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families
David Marín, 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…
Topological moduli space for germs of holomorphic foliations II: Universal deformations
David Marín, Jean-François Mattei, Éliane Salem
This work deals with the topological classification of singular foliation germs on . Working in a suitable class of foliations we fix the topological invariants…