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In a recent paper by the author (K. Yagasaki, Nonintegrability of therestricted three-body problem, submitted for publication), a technique wasdeveloped for determining whether nearly integrable systems are notmeromorphically Bogoyavlenskij-integrable such that the first integrals andcommutative vector fields also depend meromorphically on the small parameter.Here we continue to demonstrate the technique for some classes of dynamicalsystems. In particular, we consider time-periodic perturbations ofsingle-degree-of-freedom Hamiltonian systems and discuss a relationship of thetechnique with the subharmonic Melnikov method, which enables us to detect theexistence of periodic orbits and their stability. We illustrate the theory forthe periodically forced Duffing oscillator and two more additional examples:second-order coupled oscillators and a two-dimensional system of pendulum-typesubjected to a constant torque.

Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits