6 problems

The magnetic flows under consideration are defined on spheres $S^{n-1}$, with dimension parameter $n$ and magnetic parameters $\kappa$ as in the preceding construction. Complete-in…

Let $m$ be the mass of a material point moving on the sphere $S^{n-1}\subset\mathbb{R}^n$, let the point be placed in a constant homogeneous magnetic field described by the paramet…

Let $S^{n-1}\subset\mathbb{R}^n$ be the sphere, and consider the magnetic system obtained by restricting the motion in a constant homogeneous magnetic field to $S^{n-1}$. Integrabi…

Let $(S^2,g,\sigma)$ be a symplectic magnetic system. For $m>0$, define the magnetic curvature on the energy level $\Sigma_m$ by … Assume that $K_m$ is positive. Contact-type conje…

Arnold's conjecture. When $\sigma$ is symplectic and $\epsilon>0$ is sufficiently small, the lower bounds on the number of periodic orbits on $P_\epsilon$ are governed by Morse the…

Let $S^2$ carry a symplectic magnetic field, and let $\Sigma_c$ be an energy level of the corresponding magnetic flow. Suppose that the magnetic curvature is positive. Contact-type…