| Abstract: |
| The motion of a charged particle in an electromagnetic field is governed by the Lorentz force equation (LFE), a classical model independently introduced by Poincar\`{e} and Planck in the early twentieth century. It has been known since then that the periodic solutions -- corresponding to particles traveling in closed orbits -- can be formally obtained as critical points of the relativistic action functional. However, the action functional becomes nonsmooth as the speed of the particle approaches the speed of light. Thus, a rigorous critical point theory for the nonsmooth action functional has only recently been developed. In this talk, I will present some recent advances in the variational study of the LFE in collaboration with Manuel Garz\`{o}n (ICMAT, Madrid). |
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