Generic density of periodic orbits of area-preserving maps on punctured
surfaces
Generic density of periodic orbits of area-preserving maps on punctured
surfaces
We study the dynamics of area-preserving maps in a non-compact setting. We show that the $C^{\infty}$-closing lemma holds for area-preserving diffeomorphisms on a closed surface with finitely many points removed. As a corollary, a $C^{\infty}$-generic area-preserving diffeomorphism on such a surface has a dense set of periodic points. For area-preserving …