Geometry of Integrable Systems

Igor Mencattini is an Associate Professor at the Institute of Mathematics and Computer Science (ICMC) at the University of São Paulo, São Carlos campus. His area of expertise is mathematical physics, with an emphasis on the geometrical and algebraic aspects of classical mechanical systems. He earned his PhD (2005) from Boston University, and conducted post-doc studies in Germany and Italy.Alessandro Arsie is a Professor of Mathematics in the Department of Mathematics and Statistics at the University of Toledo, USA. His current research interests focus on Geometric and Algebraic techniques in Mathematical Physics and Differential Geometry. He earned his PhD (2001) from the Scuola Internazionale Superiore di Studi Avanzati (SISSA) in Trieste, Italy and conducted post-doctoral studies in Italy and in the USA.

• Part I: Preliminary material.- Symplectic Geometry.- Elements of Poisson Geometry.- Hamiltonian G-actions and the Marsden-Weinstein-Meyer reduction.- Lagrangian fibrations and integrable systems.- Elements of Bi-Hamiltonian Geometry.- Bibliographical Notes.- Part II: A Sample of Classical Integrable Systems.- Rigid bodies.- The Toda System.- Calogero-Moser Systems.- Appendix A: Elements of Symplectic Linear Algebra.- Appendix B: Elements of Differential Geometry.- Appendix C: Lie Groups, Lie Algebras, and Fiber Bundles.- Appendix D: Cotangent Lifts.- Bibliography.- Index.