  We prove the Conley conjecture for cotangent bundles of oriented, closed
manifolds, and Hamiltonians which are quadratic at infinity, i.e., we show that
such Hamiltonians have infinitely many periodic orbits. For the conservative
systems, similar results have been proved by Lu and Mazzucchelli using convex
Hamiltonians and Lagrangian methods. Our proof uses Floer homological methods
from Ginzburg's proof of the Conley Conjecture for closed symplectically
aspherical manifolds.
