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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.

MSC:
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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References:
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