3 problems

Let $M$ be the configuration manifold, let $L$ be the corresponding magnetic Lagrangian, and let $\Sigma_{\kappa}$ be the energy hypersurface at energy $\kappa$. The lowest Mañé cr…

Let $s_0$ be the critical speed associated with a magnetic system $({\mathtt{g}},\sigma)$, and let $s$ satisfy $0<s<s_0$. A contractible closed $({\mathtt{g}},\sigma)$-geodesic is…

Let $M$ be a manifold with Riemannian metric ${\mathtt{g}}$ having at least one pair of conjugate points. A closed $2$-form $\sigma$ and a value $s>0$ determine the magnetic flow…