Nonintegrability of Nearly Integrable Dynamical Systems Near Resonant Periodic Orbits

In a recent paper by the author (K. Yagasaki, Nonintegrability of restricted three-body problem, submitted for publication), technique was developed determining whether nearly integrable systems are not meromorphically Bogoyavlenskij-integrable such that first integrals and commutative vector fields also depend on small parameter. Here we continue to demonstrate some classes dynamical systems. particular, consider time-periodic perturbations single-degree-of-freedom Hamiltonian discuss relationship with subharmonic Melnikov method, which enables us detect existence periodic orbits their stability. We illustrate theory periodically forced Duffing oscillator two more additional examples: second-order coupled oscillators two-dimensional system pendulum-type subjected constant torque.