  We consider time-periodic perturbations of single-degree-of-freedom
Hamiltonian systems and study their real-meromorphic nonintegrability in the
Bogoyavlenskij sense using a generalized version due to Ayoul and Zung of the
Morales-Ramis theory. The perturbation terms are assumed to have finite Fourier
series in time, and the perturbed systems are rewritten as higher-dimensional
autonomous systems having the small parameter as a state variable.We show that
if the Melnikov functions are not constant, then the autonomous systems are not
real-meromorphically integrable near homo- and heteroclinic orbits. Our result
is not just an extension of previous results for homocliic orbits to
heteroclinic orbits and provides a stronger conclusion than them for the case
of homoclinic orbits. We illustrate the theory for two periodically forced
Duffing oscillators and a periodically forced two-dimensional system.
