ANALYSIS SEMINAR

 

 

“The Sharkovskii Theorem”

 

 

 

By

 

OĞUZHAN YÖRÜK

(BİLKENT UNIVERSITY)

(Senior Project Presentation)

 

 

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.