Many closed K-magnetic geodesics on $${\mathbb {S}}^2$$

Abstract In this paper we adopt an alternative, analytical approach to Arnol’d problem [4] about the existence of closed and embedded K -magnetic geodesics in round 2-sphere $${\mathbb {S}}^2$$ S 2 , where $$K: {\mathbb {S}}^2 \rightarrow {R}}$$ K : → R is a smooth scalar function. particular, use Lyapunov-Schmidt finite-dimensional reduction coupled with local variational formulation order get some multiplicity results bypassing symplectic geometric tools such as celebrated Viterbo’s theorem [21] Bottkoll [7].