On the generic Conley conjecture

TL;DR

This paper proves the generic Conley conjecture, showing that for broad classes of symplectic manifolds, Hamiltonian diffeomorphisms typically have infinitely many simple contractible periodic orbits.

Contribution

It establishes the generic Conley conjecture for a wide range of symplectic manifolds, advancing understanding of periodic orbits in Hamiltonian dynamics.

Findings

Proved the generic Conley conjecture for many symplectic manifolds.

Showed that Hamiltonian diffeomorphisms typically have infinitely many periodic orbits.

Extended the conjecture's validity to broader classes of manifolds.

Abstract

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.