The Hofer-Zehnder conjecture on infinitely many periodic orbits

Let $(M,\omega)$ be a compact symplectic manifold, and let a Hamiltonian map on $M$ have more fixed points than are necessarily required by the V. Arnold conjecture. Hofer-Zehnder conjecture. Every such Hamiltonian map possesses infinitely many periodic orbits. This conjecture concerns the relationship between Hamiltonian dynamics and the topology of the ambient symplectic manifold; its precise non-degenerate and Floer-theoretic formulations remain the subject of ongoing research.