  In this paper, we treat an open problem related to the number of periodic
orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds, so-called
generic Conley conjecture. Generic Conley conjecture states that generically
Hamiltonian diffeomorphisms have infinitely many simple contractible periodic
orbits. We prove generic Conley conjecture for very wide classes of symplectic
manifolds.

Symplectic Geometry;Dynamical Systems