Chapter 10.6, Problem 4E

Interpretation Introduction

Interpretation:

Consider the iteration pattern of all possible period $\text{-4}$ orbits for the logistic map or any other unimodal map governed by the U-sequence.

1. To show only two patterns RLL and RLR are possible for period $\text{-4}$ orbits.

2. To show that the period $\text{-4}$ orbit with pattern RLL always occurs after RLR, i.e., at a larger value of r.

Concept Introduction:

• The logistic map is a difference function of the unit interval and it is super stable at period $\text{2 - R}$ cycle.

• The parameter $\text{r > 3}$ in the logistic mapping consist of many sequence, the upper area of the fixed point is named by $\text{R}$ and lower area below the fixed point is named by $\text{L}$. The combination of the sequence of the logistic map at $\text{r > 3}$ is named by $\text{RL}$.