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On the minimal action function of autonomous Lagrangians associated to magnetic fields. (English) Zbl 0949.37033
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.

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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