Rigorous analyses of windows in a symmetric circuit

The two types of windows generated in a symmetric circuit are investigated. By using a degeneration technique, the authors derive a Poincare map strictly as a one-dimensional map. They make clear the mechanisms of these two types of windows and prove rigorously that they appear alternately and infinitely inside some windows, under some reasonable assumptions, by utilizing a certain scaling structure on the Poincare map. The generation of these windows would be universal in symmetric chaos-generating systems, because this circuit is extremely simple