Program of the BFZ Seminar on April 24, 2015

Anatoly Neishtadt (Loughborough University): Passages through resonances and capture into resonance in dynamics of charged particles

Abstract: Small perturbations imposed on an integrable system cause a slow evolution. In the process of this evolution the system may pass through a state of a resonance. The phenomenon of capture into resonance consists in the system starting to evolve in such a way as to preserve the resonance property once it has arisen. The class of perturbations for this phenomenon to occur includes both non-Hamiltonian perturbations and slow change of parameters of Hamiltonian systems. In the talk, a general theory of passages through resonances and captures into resonance, as well as several examples of these phenomena in problems of charged particles acceleration, will be presented.

Giuseppe Mingione (Universita' di Parma): Recent progresses in nonlinear potential theory

Abstract: Nonlinear potential theory aims at reproducing for nonlinear equations the classical results from linear potential theory about fine properties of harmonic functions and integrability properties of solutions to linear elliptic equations. I will present a number of recent results, obtained in collaboration with Tuomo Kuusi, aimed at giving sharp pointwise bounds for solutions to nonlinear elliptic and parabolic equations in terms of linear and nonlinear potentials. A number of corollaries will be also given.

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