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Explore the third lecture in a series on integrable Hamiltonian systems, focusing on the quasi-Poisson double case and specific examples involving SU(n) symplectic leaves. Delve into advanced mathematical concepts examining Poisson reductions of integrable 'master systems' on classical doubles of semisimple, connected and simply connected compact Lie groups. Learn about the compact counterparts of the trigonometric Ruijsenaars-Schneider system through detailed mathematical analysis. Build upon the previous lectures' exploration of degenerate integrability on Poisson quotients and the interpretation of reduced systems as Ruijsenaars-Schneider type many-body systems with spin degrees of freedom. Gain insights into this complex mathematical topic presented at the Erwin Schrödinger International Institute's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications."
