On the minimal action function of autonomous Lagrangians associated to magnetic fields (Q1961843)
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scientific article; zbMATH DE number 1394702
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the minimal action function of autonomous Lagrangians associated to magnetic fields |
scientific article; zbMATH DE number 1394702 |
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On the minimal action function of autonomous Lagrangians associated to magnetic fields (English)
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10 December 2000
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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.
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Hall effect
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Lagrangian systems
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two-dimensional theories
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