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The Logistic Function Part II: Topological Conjugacy

  • Richard A. Holmgren
Chapter
  • 748 Downloads
Part of the Universitext book series (UTX)

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.)

Keywords

Commutative Diagram Periodic Point Sensitive Dependence Text Dynamical Prime Period 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Richard A. Holmgren
    • 1
  1. 1.Department of MathematicsAllegheny CollegeMeadvilleUSA

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