Fake saddles and their transition maps
David Marín · Electronic journal of qualitative theory of differential equations · 2026
We study degenerate singular points of planar vector fields inside a (degenerate) flow box. These kind of singularities are called fake saddles and their linear parts are always zero. We characterize fake saddles with non-zero second-order jet and we give the first term of a uniform asymptotic expansion of the Poincaré map between two transverse sections to their corresponding singular fiber, determining its stability.