Periodic Points of Hamiltonian Diffeomorphisms Equal to Nondegenerate Linear Maps at Infinity

Abstract

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist condition, we prove the existence of infinitely many simple periodic points. More precisely, if such a diffeomorphism has only finitely many fixed points, then it admits simple periodic points with arbitrarily large prime periods.