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Notícias

Notícias

Colóquio: From oscillations to integrable systems and Symplectic Geometry

Publication date: 26-04-2018 11:55

Jean-Pierre Françoise

Resumo: Oscillations can be observed in many natural physical and biological phenomena. The pendulum can be used as an introduction to several mathematical concepts. Actually Jacobi created the theory of elliptic functions to solve the motion of the pendulum. His work can be revisited using symplectic geometry and Birkhoff normal form. This can be extended to the free Rigid Body motion. These are examples of integrable Hamiltonian Systems to which are associated Elliptic Fibrations in the sense of Kodaira. An interesting issue both for Symplectic Geometry and Elliptic Fibrations is to study singular fibers. We finish with some new results on the semi-global symplectic invariants related with these singularities.



Jean-Pierre Françoise (Sorbonne Univ., Paris, France)
2 de maio, quarta feira, 15h
Sala 2.4, Departamento de Matemática da FCTUC