# Exercises for Chaos Under Control

## Chapter 4: The Family Portrait of Attractors

37.[C] (a) For the tent map, take x_{0} = 0.5; plot the graph of
x_{1}, x_{2}, x_{3}, and x_{4} as functions of
s, with s ranging from 0 to 2.

(b) Compare the Bifurcation Diagram for the tent map (using TENT/BIFURCATION)
with the graphs pictured in (a). What conclusion can you make?

38. Using the results of exercise 37, verify that the band-merging of the
Bifurcation Diagram occurs at s = sqrt(2).

39.[C] Perform several magnifications around s = 1 and x = 1/2, using
TENT/BIFURCATION. Show both branches of the band-merging have band-merging
branches themselves.

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