On the generic Conley conjecture

In this paper, we treat an open problem related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds, the so-called (generic) Conley conjecture. The generic Conley conjecture states that generically Hamiltonian diffeomorphisms have infinitely many simple contractible periodic orbits. We prove the generic Conley conjecture for very wide classes of symplectic manifolds. Our proof is based on applications of the Birkhoff-Moser fixed point theorem and Floer homology theory.

Automated summary

This paper addresses an open problem known as the (generic) Conley conjecture, which is related to the number of periodic orbits of Hamiltonian diffeomorphisms on closed symplectic manifolds. The generic Conley conjecture states that Hamiltonian diffeomorphisms typically have infinitely many simple contractible periodic orbits. The proof provided in this paper relies on applications of the Birkhoff-Moser fixed point theorem and Floer homology theory.