  In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to
integrability of nearly integrable dynamical systems near regular level sets,
submitted for publication, and K.~Yagasaki, Nonintegrability of nearly
integrable dynamical systems near resonant periodic orbits, submitted for
publication), two different techniques which allow us to prove the
real-analytic or complex-meromorphic nonintegrability of forced nonlinear
oscillators having the form of time-periodic perturbations of
single-degree-of-freedom Hamiltonian systems were provided. Here the concept of
nonintegrability in the Bogoyavlenskij sense is adopted and the first integrals
and commutative vector fields are also required to depend real-analytically or
complex-meromorphically on the small parameter. In this paper we review the
theories and continue to demonstrate their usefulness. In particular, we
consider the periodically forced damped pendulum and prove its nonintegrability
in the above meaning.
