Fake saddles and their transition maps
Abstract
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.
Fields of Study & Subjects
Artificial Intelligence in Games
Publication details
- Journal / source
- Electronic journal of qualitative theory of differential equations
- Issue
- 5
- Pages
- 1–10
- Publication date
- 1 January 2026
- Language
- EN