  In this article, we study the Hamiltonian dynamics on singular symplectic
manifolds and prove the Arnold conjecture for a large class of $b^m$-symplectic
manifolds. Novel techniques are introduced to associate smooth symplectic forms
to the original singular symplectic structure, under some mild conditions.
These techniques yield the validity of the Arnold conjecture for singular
symplectic manifolds across multiple scenarios. More precisely, we prove a
lower bound on the number 1-periodic Hamiltonian orbits for $b^{2m}$-symplectic
manifolds depending only on the topology of the manifold. Moreover, for
$b^m$-symplectic surfaces, we improve the lower bound depending on the topology
of the pair $(M,Z)$. We then venture into the study of Floer homology to this
singular realm and we conclude with a list of open questions.
