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A Poincaré-Birkhoff theorem for asymptotically linear Hamiltonian diffeomorphisms (Leonardo Masci)
Speaker: Leonardo Masci

Abstract: The celebrated Poincaré-Birkhoff theorem on area-preserving maps of the annulus is of fundamental importance in the fields of Hamiltonian dynamics and symplectic topology. In this talk I will formulate a generalization of the Poincaré-Birkhoff theorem, which applies to asymptotically linear Hamiltonian systems on linear phase space, in the spirit of Amann, Conley and Zehnder. In order to explain some elements of the proof, I will explore the main difficulties in setting up a Floer homology for this class of Hamiltonian systems, and touch on two techniques which can be combined to relate the filtered Floer homologies of different iterates of the same asymptotically linear Hamiltonian diffeomorphism.

Date : Wed, Apr 24

Time: 11:00

Place: Seminar room 4, 3rd floor