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The Quadratic Family and the Mandelbrot Set

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

Abstract

We return once again to the study of the dynamics of quadratic functions. In this chapter, we consider the quadratic family q c (z)=z2+c. We demonstrated in Exercise 9.5 that all real quadratic functions are topologically conjugate to a real polynomial of the form q c (x)=x2+c for some c. This fact extends to the complex quadratic polynomials; all complex quadratic polynomials are topologically conjugate to a polynomial of the form q c (z)=z2+c. (The reader is asked to show this in Exercise 15.1.) We will take direction for our study of the quadratic family from our previous work with the logistic map h r (x)=rx(1 − x).

Keywords

Periodic Point Inverse Image Real Polynomial Prime Period Mathematica Program 
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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