Cheap Complex Limit Cycles
Complex Variables
2018-04-13 v3
Abstract
Consider a holomorphic foliation with singularities of a 2-dimensional complex manifold. In this article we prove a new sufficient condition for this foliation to have countably many homologically independent complex limit cycles. In particular, if all leaves of a foliation are dense in the phase space, and it has a complex hyperbolic singular point, then it has infinitely many homologically independent complex limit cycles.
Cite
@article{arxiv.1702.00897,
title = {Cheap Complex Limit Cycles},
author = {Nataliya Goncharuk and Yury Kudryashov},
journal= {arXiv preprint arXiv:1702.00897},
year = {2018}
}