The Sharkovskii Theorem
Abstract: This is a Senior Project presentation. The Sharkovskii Theorem provides a special order of all natural numbers such that, for a continuous function f on the real line, once the function f has orbits of length n than it has orbits of lengths all other natural numbers that are dominated by n in this special order. At the beginning of this special order there is the number 3 and hence, this theorem has as consequence the fact that, if the function f has orbits of lengths 3 then it has orbits of any length, which is one of the definition of chaotic behavior under iteration. A detailed proof of this theorem will be presented.
Date: Tuesday, December 16, 2014
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.