Sarkovskii’s Theorem

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


Consider the function \( p(x) = - \tfrac{3}{2}{x^2} + \tfrac{5}{2}x + 1 \). It is easy to see that p(0) = 1, p(1) = 2, and p(2) = 0. So {0, 1, 2} is an orbit with period three. It is reasonable to ask how many other periodic points p(x) has and what prime periods are represented.


Natural Number Chaotic Dynamics Closed Interval Periodic Point Nest Sequence 
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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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