A Higher Dimensional Generalization of the Birkhoff Attractor

Explore a higher dimensional generalization of the Birkhoff attractor in this 59-minute lecture by Vincent Humilière at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the application of the spectral metric, introduced in Claude Viterbo's talk, as a powerful tool for studying the dynamics of both symplectic maps and conformal symplectic maps. Discover how this approach extends to damped Hamiltonian systems and enables the generalization of the classical Birkhoff attractor, previously confined to the 2-dimensional annulus, to higher dimensions. Gain insights into ongoing joint research with Marie-Claude Arnaud and Claude Viterbo, expanding the understanding of dynamical systems and their applications in mathematical physics.

Vincent Humilière - A higher dimensional generalization of the Birkhoff attractor