AbstractThis paper shows that in a certain type of amplitude‐controlled oscillator using a pulsewidth controller, correspondence of the Poincaré map with the cut map and logistic map can be obtained. It is proven almost analytically that the Poincaré map is ergodic if it becomes a cut map. By a computer‐assisted analysis, it is proven that chaos in the sense of Li‐Yorke is generated if it is a logistic map. Further, the validity of the analysis is confirmed by a circuit exp