Magnetic flows on negatively curved surfaces with nonpositive magnetic curvature retain topological transitivity, dense periodic orbits, and equilibrium states, but the natural magnetic distance is not symmetric and fails the triangle inequality.
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Surfaces with nonpositive magnetic curvature
Magnetic flows on negatively curved surfaces with nonpositive magnetic curvature retain topological transitivity, dense periodic orbits, and equilibrium states, but the natural magnetic distance is not symmetric and fails the triangle inequality.