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math.DS2025
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…
math.DS2025
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…