Limit cycles and invariant algebraic curves
Dynamical Systems
2026-01-01 v2
Abstract
We give lower bounds in terms of~ for the number of limit cycles of polynomial vector fields of degree~ having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles we obtain a new recurrent property for the Hilbert numbers. Finally, we apply our results to two important families of models: Kolmogorov systems and a general family of systems appearing in Game Theory.
Cite
@article{arxiv.2510.11705,
title = {Limit cycles and invariant algebraic curves},
author = {Armengol Gasull and Paulo Santana},
journal= {arXiv preprint arXiv:2510.11705},
year = {2026}
}