Areas on the space of smooth probability density functions on S2

J. C. Ruíz-Pantaleón, Pablo Suárez-Serrato

Abstract: We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.