Sarkovskii’s Theorem

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

Abstract

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.

Keywords

Natural Number Chaotic Dynamics Closed Interval Periodic Point Nest Sequence
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