New solutions of the Poincar\'e Center Problem in degree 3
Algebraic Geometry
2025-04-14 v2 Dynamical Systems
Abstract
Let be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi-homogeneous we we present new criteria that guarantee Darboux integrability. We use this to construct previously unknown components of the center variety in degree 3.
Keywords
Cite
@article{arxiv.2409.01751,
title = {New solutions of the Poincar\'e Center Problem in degree 3},
author = {Hans-Christian von Bothmer},
journal= {arXiv preprint arXiv:2409.01751},
year = {2025}
}
Comments
Includes 5 figures; updated references; revised section on the inverse problem; the role of singularities is emphasized throughout the paper