Mean action and the Calabi invariant.

par Abror Pirnapasov (abror.pirnapasov@ens-lyon.fr)

vendredi 10 févr. 2023, 10:30 → 11:30 Europe/Paris

112 (ICJ)

Hutchings used Embedded Contact Homology to show the following for area-preserving disc diffeomorphisms that are a rotation near the boundary of the disc: if the asymptotic mean action on the boundary is greater than the Calabi invariant, then the infimum of the mean action of the periodic points is less than or equal to the Calabi invariant. In this talk, I explain how to extend this result to all orientation and area-preserving disc diffeomorphisms. I also introduce a more general result for area-preserving disc diffeomorphisms with only one periodic point. This is joint work with David Bechara, Barney Bramham, and Patrice Le Calvez.