Magnetic geodesic flows interpolate between sub-Riemannian and magnetic vector field flows, magnetomorphism actions produce Poisson-commuting integrals, and totally magnetic submanifolds are closed under fixed points and intersections.
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Defines Mañé's critical value for exact magnetic systems on Hilbert manifolds, computes it for the new M2HS, proves an infinite-dimensional magnetic Hopf-Rinow theorem, and uses it to construct global conservative weak solutions by embedding into a magnetic system on the three-sphere.
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Topics in Magnetic Geometry: Interpolation, Intersections and Integrability
Magnetic geodesic flows interpolate between sub-Riemannian and magnetic vector field flows, magnetomorphism actions produce Poisson-commuting integrals, and totally magnetic submanifolds are closed under fixed points and intersections.
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On Ma\~n\'e's critical value for the two-component Hunter-Saxton system and a infnite dimensional magnetic Hopf-Rinow theorem
Defines Mañé's critical value for exact magnetic systems on Hilbert manifolds, computes it for the new M2HS, proves an infinite-dimensional magnetic Hopf-Rinow theorem, and uses it to construct global conservative weak solutions by embedding into a magnetic system on the three-sphere.