Super-stable Kneading Sequences with Double Cycles in 1D Bimodal Maps

Abstract

It is well known that a super-stable kneading sequence (SSKS) is an important concept, all SSKSs in bimodal maps forms joints in the corresponding symbolic dynamics, it decides the multiplication table of star products, which the n-tupling bifurcations to chaos can be investigated and Feigenbaum’s metric universalities can be measured and reconstructed, this SSKSs have form   which are periodic with single cycle. However, in fact, the SSKSs in bimodal maps have another form with double cycles which are little mentioned and researched, they have the same position and significance as the single cycle SSKS. In the paper, we presented the number of admissible SSKSs with period-n and the joints graph on the parameter plane.