Analysis of the limit values of chaos degree for infinite number of partitions in asymmetric tent maps

Abstract

Chaos degree is proposed as a measure of chaos that can be computed from a data series. It is known that the value of chaos degree is unstable under the influence of partition. Therefore, one of mathematical interests is whether chaos degree has a limit value or not when the number of partitions is infinite. In this study, we analytically derived the limit values of chaos degree for asymmetric tent maps, and found that the limit values differ significantly when the parameter is an irrational and rational number.