English

Bounded limit cycles of polynomial foliations of $\mathbb CP^2$

Complex Variables 2018-04-13 v1 Dynamical Systems

Abstract

In this article we prove in a new way that a generic polynomial vector field in C2\mathbb C^2 possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain.

Keywords

Cite

@article{arxiv.1504.03313,
  title  = {Bounded limit cycles of polynomial foliations of $\mathbb CP^2$},
  author = {Nataliya Goncharuk and Yury Kudryashov},
  journal= {arXiv preprint arXiv:1504.03313},
  year   = {2018}
}