“The
Sharkovskii Theorem”
By
OĞUZHAN YÖRÜK
(BİLKENT UNIVERSITY)
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
Time: 15:40
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the
seminar.