The Logistic Function Part II: Topological Conjugacy
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We continue our investigation of the logistic function by showing that h(x) = 4x(1 − x) is chaotic on [0,1]. Unfortunately, proving this directly from the definition is a relatively difficult task. Consequently, we will show instead that the dynamics of h on [0,1] are the same as the dynamics of the tent map on [0,1]. Mathematically speaking, we say that h on [0,1] is topologically conjugate to the tent map on [0,1]. (The tent map was introduced and shown to be chaotic in Exercise 8.9 on page 86.)
KeywordsCommutative Diagram Periodic Point Sensitive Dependence Text Dynamical Prime Period
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