Disappearance of chaos and integrability in an externally modulated nonlinear oscillator

The nonexistence of chaotic motions in a nonlinear oscillator with an externally modulated frequency which is exactly solvable is demonstrated analytically. By means of numerical investigations it is shown that the stabilizing effect is also present when the driving force belongs to a wide class not included in the demonstration. Surprisingly, chaotic behavior, present when the force is a periodic $\delta$ function, is destroyed if the amplitude of the pulses depends on the coordinate.