Real holomorphic curves and invariant global surfaces of section

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.

36 pages

References in corpus (2)

• A dynamical characterization of universally tight lens spaces
• On reversible maps and symmetric periodic points