Cheap Complex Limit Cycles

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.

References in corpus (1)

• Bounded limit cycles of polynomial foliations of $\mathbb{C}{P}^2$