On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields
Dynamical Systems
2024-05-22 v6
Abstract
It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytical vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney's topology.
Keywords
Cite
@article{arxiv.2303.00220,
title = {On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields},
author = {Paulo Santana},
journal= {arXiv preprint arXiv:2303.00220},
year = {2024}
}