Arnold conjecture for compact symplectic manifolds

Let $(M,\omega)$ be a compact symplectic manifold, and let $H:\mathbb{R}\times M \to \mathbb{R}$ be a time-dependent Hamiltonian function. Suppose that the solutions of period $1$ of the associated Hamiltonian system are non-degenerate. Let $\mathcal{P}(H)$ denote the set of $1$-periodic orbits. Arnold conjecture. The number of these orbits satisfies

$$\#\mathcal{P}(H) \geq \sum_i \dim H_i(M;\mathbb{Z}_2).$$

This is the classical lower bound for non-degenerate 1-periodic Hamiltonian orbits in terms of the total mod-$2$ Betti number. The paper proves analogous results for broad classes of singular, including $b^{2m}$-symplectic, manifolds, while the statement here is presented as the classical symplectic model motivating that work.