On the minimal action function of autonomous Lagrangians associated to magnetic fields
The authors study a special Lagrangian on the two-dimensional torus with two degrees of freedom and periodic in each spatial coordinate. There exists a nontrivial magnetic potential vector but there is no electrostatic potential. This model appears in phenomena related to the Hall effect. The dynamical properties of the Euler-Lagrange field generated by the Lagrangian associated to a magnetic field is studied. The structure of Mather sets, that is, sets that are supports of minimizing measures for the corresponding autonomous Lagrangian, is investigated.
scientific article; zbMATH DE number 1394702