Many closed K-magnetic geodesics on S^2

In this paper we adopt an alternative, analytical approach to Arnol’d problem about the existence of closed and embedded K-magnetic geodesics in the round 2-sphere ^2, where :^2→ℝ is a smooth scalar function. In particular, we use Lyapunov-Schmidt finite-dimensional reduction coupled with a local variational formulation in order to get some existence and multiplicity results bypassing the use of symplectic geometric tools such as the celebrated Viterbo’s theorem and Bottkoll results.