Fake saddles and their transition maps

2025/09/16 by Marín, David
#34C05 #34D10 #34D20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.12941

Abstract

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 zero. We characterize fake saddles with non-zero second order jet and we give the first term of an uniform asymptotic expansion of the Poincaré map between two transverse sections to their corresponding singular fiber, determining its stability.

Citations

• The criticality of reversible quadratic centers at the outer boundary of its period annulus
• Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: Coefficient properties

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