March 9, 2022 talk by A.Tsiganov "Integrable metrics with higher order invariants on the sphere, ellipsoid and plane"

• Slides

Abstract: We will discuss how to apply various symplectic maps and Maupertuis principle to construct new integrable metrics (geodesic flows).
As an example, we will present a few equivalent metrics on 2D sphere, ellipsoid and plane with cubic, quartic and sextic invariants.
By materials of Dynamics in Siberia conference, see presentation in
https://www.researchgate.net/publication/359003956_On_integrable_geodesic_flows_sphere_ellipsoid_and_hyperboloid