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arXiv · 1702.00897

Cheap Complex Limit Cycles

Nataliya Goncharuk·Yury Kudryashov
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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.

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Nataliya Goncharuk, Yury Kudryashov. 2017-07-19. Cheap Complex Limit Cycles. https://doi.org/10.1088/1361-6544%2Faa999a

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