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arXiv · 1501.04853

Real holomorphic curves and invariant global surfaces of section

Urs Frauenfelder·Jungsoo Kang
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Abstract

In this paper we prove that a dynamically convex starshaped hypersurface in $\mathbb{C}^2$ which is invariant under complex conjugation admits a global surface of section which is invariant under conjugation as well. We obtain this invariant global surface by embedding $\mathbb{C}^2$ into $\mathbb{CP}^2$ and applying a stretching argument to real holomorphic curves in $\mathbb{CP}^2$. The motivation for this result arises from recent progress in applying holomorphic curve techniques to gain a deeper understanding on the dynamics of the restricted three body problem.

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Urs Frauenfelder, Jungsoo Kang. 2015-01-20. Real holomorphic curves and invariant global surfaces of section. https://arxiv.org/abs/1501.04853

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