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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Constructs infinite-dimensional spaces of exact magnetic systems of strong geodesic type on closed manifolds, proving existence of null-homologous embedded periodic orbits with negative action below the strict Mañé critical value and hence non-contact type energy surfaces, resolving the conjecture.
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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 the contact type conjecture for exact magnetic systems
Constructs infinite-dimensional spaces of exact magnetic systems of strong geodesic type on closed manifolds, proving existence of null-homologous embedded periodic orbits with negative action below the strict Mañé critical value and hence non-contact type energy surfaces, resolving the conjecture.