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Bibliographic Details
Main Author: Marín, David
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.12941
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author Marín, David
author_facet Marín, David
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_12941
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fake saddles and their transition maps
Marín, David
Dynamical Systems
34D10, 34D20, 34C05
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.
title Fake saddles and their transition maps
topic Dynamical Systems
34D10, 34D20, 34C05
url https://arxiv.org/abs/2509.12941