Hamiltonian Evolution Equations - Where They Come From, What They Are Good For

Abstract: I start with a brief survey of examples of (non-linear) Hamiltonian evolution equations describing the dynamics of a variety of physical systems with infinitely many degrees of freedom. Among examples are the Vlasov-, Euler-, Hartree- and Hartree-Fock equations. I then focus on the example of Hartree(-Fock) equations describing the  dynamics of stars in a mean-field limit.

Among other results, I sketch a dynamical approach to the problem of stability of boson stars and of white dwarfs (Chandrasekhar limit).- Results obtained in collaboration with Enno Lenzmann. If time permits I will then consider Hamiltonian equations of motion

describing a heavy point-particle coupled to a wave medium. If the speed of the particle exceeds the speed of wave propagation in the medium the particle tends to emit Cherenkov radiation. This results in a deceleration of the particle until its speed has dropped to a value smaller or equal to the speed of wave propagation in the medium, where after its motion is ballistic. This provides an example of "Hamiltonian Friction".- Results worked out in collaboration with Gang Zhou.