Periodic orbits of weakly exact magnetic flows

Osvaldo Osuna
2013 Nonlinear Analysis and Differential Equations  
For a weakly exact magnetic flows with a bounded primitive on a closed Riemannian manifold, we prove the existence of periodic orbits in almost all energy levels below of the Mañé's critical value. Mathematics Subject Classification is a Riemannian universal covering of (M, g), thus the flow of L coincide with the lift of the magnetic flow (g, Ω) therefore is complete. Recall that on a boundaryless, complete Riemannian manifold N an autonomous Lagrangian is a smooth function, L : T N → R such
more » ... at L is convex and superlinear when restricted to any fiber (see [2] Note if a weakly exact magnetic flow has a bounded primitive θ, then our Lagrangian L satisfies the above conditions (see [2] for details).
doi:10.12988/nade.2013.13011 fatcat:4qnns3j7qnf45j6rswsu3eby34