Olga Bernardi (Università di Padova) and Vincent Humilière (Sorbonne Universitè)

Abstract: In his study of dissipative maps on the cylinder, G.D. Birkhoff constructed in 1932 a “minimal” closed, connected and invariant subset associated with any such map. This subset, now called Birkhoff attractor, has since been extensively studied by many authors, e.g. M. Charpentier and P. Le Calvez. In these talks, Olga will first introduce the Birkhoff attractor and discuss its topological and dynamical complexity in the case of dissipative billiards (joint work with L. Baracco, A. Florio. M. Leguil and A. Nardi). In the second part, Vincent will present a higher dimensional extension of the Birkhoff attractor, recently obtained with M.-C. Arnaud and C. Viterbo, using tools from symplectic topology.

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