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Seminar in Mathematical physics and related subjects: “Tori or Spheres? An introduction to the generalization of Poincaré-Birkhoff Theorem in higher dimension”

Thursday, April 4, 2019, 14:30 - Room 1BC45 - Paolo Gidoni

ARGOMENTI: Seminars

Paolo Gidoni (Padova)
“Tori or Spheres? An introduction to the generalization of Poincaré-Birkhoff Theorem in higher dimension”
Thursday, April 4, 2019, 14:30-15:30
Room 1BC45

Absract
The celebrated Poincaré-Birkhoff Theorem, with its several applications, attests the relevance of twist as boundary condition for planar Hamiltonian systems. But what becomes of the twist condition when we try to extend this result to higher dimensions? Whereas on the plane the notion of twist is quite intuitive, the same cannot be said about twist in higher dimensions. Indeed, due to the special nature of the plane, the Poincaré-Birkhoff Theorem can be seen as the overlap of several distinct higher dimensional results. In this seminar we will overview the two main approaches to this issue.