On the problem of convexity for the restricted three-body problem around the heavy primary
type: Item
instance of: scholarly article
title: On the problem of convexity for the restricted three-body problem around the heavy primary
zbMATH Open document ID: 1503.70008
author: Otto van Koert
author: Lei Zhao
author: Urs Frauenfelder
published in: Hokkaido Mathematical Journal
publication date: 2022-10-27T00:00:00Z
review text: The authors consider the energy surface of the planar rotating Kepler problem for energy below the first critical level. They show that, outside a small neighborhood of the collisions, there is a convex symplectic embedding of the double cover of the component of the energy surface around the heavy body into \({\mathbb R}^4\). This approach is relevant to attack the Birkhoff conjecture about the existence of a global surface of section in the restricted planar circular three-body problem using holomorphic curve techniques.
reviewed by: Miguel Paternain
Mathematics Subject Classification ID: 70F05
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 7608269
zbMATH Keywords: contact and symplectic topology
zbMATH Keywords: convexity
zbMATH Keywords: global surfaces of section
zbMATH Keywords: restricted three-body problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/2020-370
OpenAlex ID: W4295027058
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DOI: 10.14492/HOKMJ/2020-370
description: scientific article; zbMATH DE number 7608269