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Session S03 - Geometric and Variational Methods in Celestial Mechanics

Monday, July 12, 15:30 ~ 15:55 UTC-3

Projective Dynamics and an integrable Billiard System of Boltzmann-Gallavotti-Jauslin

Lei Zhao

Univeritat Augsburg, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A biliard model in a half plane, with the boundary line of the half plane as wall of reflection, defined via the planar Kepler problem, is shown to be integrable by Gallavotti and Jauslin who explicitely constructed an independent integral additional to the energy. The bounded dynamics of the system has been shown by Felder to carry periodic and quasi-periodic dynamics. The model is proposed as a limiting case of a set of more general models proposed by Boltzmann in order to illustrate his "ergodic hypothesis". In this talk, I shall explain that the integral of Gallavotti-Jauslin is ultimately related to the energy of an associated Kepler problem on the sphere.

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