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arXiv · 1903.03665

Recurrent Trajectories and Finite Critical Trajectories of Quadratic Differentials on the Riemann Sphere

Faouzi Thabet
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Abstract

In this paper, the focus will be on both the existence and non-existence respectively of finite critical trajectories and recurrent trajectories of a quadratic differential on the Riemann sphere. We show the connection between these two items. More precisely, we collect some criterions for the non-existence of recurrent trajectories. The first criterion is in the same vein of Jenkins Three-pole Theorem, while the second one is in relation with the so-called Level function of quadratic differentials.

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Faouzi Thabet. 2019-03-08. Recurrent Trajectories and Finite Critical Trajectories of Quadratic Differentials on the Riemann Sphere. https://arxiv.org/abs/1903.03665

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