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.
Anosov magnetic flows on surfaces
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abstract
Using the quotient bundle introduced by Wojtkowski, we give necessary and sufficient conditions for a magnetic flow on a closed, oriented surface to be Anosov.
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2026 1verdicts
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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.