• Tingueu el micròfon apagat tota l'estona excepte durant el "Cafè i galetes".
• Podeu tenir la càmera encesa si voleu, però en cas de saturaciò de línies, caldrà que la tanqueu.
• Si voleu fer una pregunta, si us plau demaneu torn a través del xat i espereu que els moderadors us donin la paraula.
• Si és possible, entreu amb antelació. Els que no useu un compte de correu de la UPC haureu d'esperar a ser admesos per accedir-hi. (Això aplica a les sessions Google Meet de la UPC).

Dia: Dimecres, 29 de març de 2023

Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.

• Hora: 16h00m

A càrrec de: Robert Cardona (UPM-ICMAT)

Títol: Periodic orbits and surfaces of section on Hamiltonian systems: from contact to stable energy level sets

Resum: The quest for periodic orbits and surfaces of section (or "Birkhoff sections") traces back to the work of Poincaré in his study of the restricted three-body problem. Proving the existence of these two objects on regular energy level sets of Hamiltonian systems has been a leading problem in the flourishing field of symplectic dynamics. In this talk, we are interested in the dynamics of non-vanishing volume-preserving vector fields on closed three-manifolds, equivalently understood as Hamiltonian vector fields along regular energy level sets. We will survey some recent striking results for the class of Reeb vector fields defined by contact forms, and present generalizations to the case of vector fields defined by stable Hamiltonian structures. Such structures appear, for example, when restricting a Hamiltonian vector field to a "stable" energy level set.

This talk is based on joint work with A. Rechtman.

Last updated: Thu Mar 23 17:20:28 2023