Fake saddles and their transition maps
Dynamical Systems
2025-09-23 v3
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 Poincar\'e map between two transverse sections to their corresponding singular fiber, determining its stability.
Keywords
Cite
@article{arxiv.2509.12941,
title = {Fake saddles and their transition maps},
author = {David Marín},
journal= {arXiv preprint arXiv:2509.12941},
year = {2025}
}