# Exercises for Chaos Under Control

## Chapter 4: Some Dust in the Tent

40.[A] For s > 2 we have seen the interval [0,1] contains many points
escaping to -infinity. Show the points not escaping to -infinity form a
Cantor set, and find the similarity dimension of this Cantor set.
Note: the dimension will be expressed in terms of the slope s.
Answer

41.[A] Let s = 4 in the tent map. To what value does x = 1/4 map?
To what value does x = 1/16 map? To what value does x = 1/64 map? Now,
suppose x_{0} = 1/4^{n}. What is x_{1}?
What is x_{2}? What are x_{n-1}, x_{n}, and
x_{n+1}?
Answer

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The Family Portrait of Attractors

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