Calculus of Variations and Geometric Measure Theory

A. Figalli - J. Palmer - A. Pelayo

Symplectic G-capacities and integrable systems

created by figalli on 04 Oct 2016


Accepted Paper

Inserted: 4 oct 2016
Last Updated: 4 oct 2016

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Year: 2016


For any Lie group $G$, we construct a $G$-equivariant analogue of symplectic capacities and give examples when $G=T^k\times R^{d-k}$, in which case the capacity is an invariant of integrable systems. Then we study the continuity of these capacities, using the natural topologies on the symplectic $G$-categories on which they are defined.