January 15, 2021 11:00 - 12:00 CET
Javier de Lucas Araujo (Assistant professor at the Department of Mathematical Methods in Physics of the Faculty of Physics of the University of Warsaw)
This talk provides a brief introduction to symplectic geometry and its applications to dynamical systems. In particular, I will explain the most fundamental notions on symplectic geometry such as the Darboux theorem, the canonical symplectic structure on the cotangent bundle, and the main properties of the so-called Hamiltonian vector fields. Concerning the applications of symplectic geometry to dynamical systems, the Liouville theorem, the Gromov’s non-squeezing theorem, and the main properties of the referred to as integrable Hamiltonian systems will be analysed.
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