2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71782We prove that either there exists at least one hamilton periodic orbit in a given energy close smooth hypersurface or there exist at least two hamilton periodic orbits in a near-by energy close smooth hypersurface. More general results also hold.Symplectic GeometryDynamical Systems32Q65,53D35,53D12text