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This paper studies robustness and an application of a one-dimensional window-map based on rotation dynamics. The map with a flat part that is called a window exhibits various superstable periodic orbits (SSPOs) and bifurcations. Using theoretical analysis, we clarify existence regions of the period of the SSPOs in parameter space. We also consider an application to an analog-to-digital converter and clarify output characteristics based on theoretical calculation. Next, we consider the case where the window has a small slope as parameter perturbation and show typical phenomena and robustness. Finally, we discuss bifurcation phenomena and robustness for the window-map based on chaos.

Robustness and an application of a one-dimensional window-map based on rotation dynamics