29 nov 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
Symplectic diffeomorphisms constitute the group of symmetries of Hamiltonian systems in classical mechanics. For this reason, the geometry associated with these diffeomorphisms has been the subject of intense study in the last decades. One of the breakthroughs in the field was the construction of so-called capacities, that is, non-trivial symplectic invariants measuring the size of sets in phase space. Many natural questions arise in this context: Are symplectic capacities unique? Is there any relationship between the capacity of a set and its volume? In this talk, we will present a joint work with Alberto Abbondandolo and Oliver Edtmair, where we relate such questions to Hamiltonian systems having a fully periodic flow.