Consider the iteration pattern of all possible period -4 orbits for the logistic map or any other unimodal map governed by the U-sequence. To show only two patterns RLL and RLR are possible for period -4 orbits. To show that the period -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 2 - R cycle. The parameter r > 3 in the logistic mapping consist of many sequence, the upper area of the fixed point is named by R and lower area below the fixed point is named by L . The combination of the sequence of the logistic map at r > 3 is named by RL .

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Chapter 10.6, Problem 4E

Interpretation Introduction

Interpretation:

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

To show only two patterns RLL and RLR are possible for period -4 orbits.

To show that the period -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 2 - R cycle.

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

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