Plenaria - Umberto Hryniewicz
Channel: Centro de Matemática
Date: 01/11/2018

"Holomorphic curves and celestial mechanics" - Umberto Hryniewicz (Universidade Federal do Rio de Janeiro)

We would like to describe how the modern methods of symplectic topology, such as pseudo-holomorphic curve theory, can be used to study celestial mechanics. Particular emphasis will be given to the planar circular restricted three-body problem. When the value of the Jacobi constant is high enough, components of the energy level covering a bounded Hill region are amenable to both Levi-Civitta or Moser regularization. Both schemes yield contact-type energy levels, allowing for the use pseudo-holomorphic curves. We will address a conjecture of Birkhoff asserting that the lift of a retrograde orbit via Levi-Civita bounds a disk-like global surface of section, and describe a version of the Poincare-Birkhoff theorem for Reeb flows which applies in the presence of a Hopf link of periodic orbits. If time permits we shall describe general results on the existence of genus zero global surfaces of section.

VI Coloquio Uruguayo de Matemática, 20–22 de diciembre de 2017.

https://6coloquio.cmat.edu.uy/

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