Abstract
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.)
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© 1996 Springer Science+Business Media New York
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Holmgren, R.A. (1996). The Logistic Function Part II: Topological Conjugacy. In: A First Course in Discrete Dynamical Systems. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8732-7_9
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DOI: https://doi.org/10.1007/978-1-4419-8732-7_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94780-8
Online ISBN: 978-1-4419-8732-7
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