Constructing Multi-Branches Complete Chaotic Maps That Preserve Specified Invariant Density

Figure 3

Illustration of Example 4.1.

(a) Invariant measure 𝜇 and its inverse

(b) Branching functions

(c) 𝐹 resulted from 𝐺={𝑥,𝑥,𝑥}

(d) 𝜙(𝑥) and frequency of 𝑓(𝑥)