The Warwick Mathematics Society Website

User login

Upcoming events

Add to iCalendar
more

There are 346 members of the Warwick Mathematics Society, of which 3 are new today!
We're 69% of the way toward our target of 500 members.
You can join up on the UWSU website.

Discussion groups [Dg]:=<Real Dynamics and Sharkovskii's Theorem>

83cellular-f10.gif
Monday 12th November, 7:30 pm - 9:00 pm

Take a function $ f:\mathbb{R}\to\mathbb{R} $ and start with a number $ x $, immediately our function presents us with a new point $ f(x) $: and, being rather inquisitive, we can't help but wonder what happens to this one under $ f $, and by extension the next, and the next and so on...

What is the long term behavior of $ x $ under $ f $? Will it stop? Will it get trapped in some cycle? How many such cycles are there? And what happens if it misses out on cycles altogether?

These questions are at least in part answered by Sharkovskii's theorem- an extraordinarily powerful and, at first glance, rather unexpected theorem with a quite elementary proof. A result tying together several properties of our system and dancing on the fringe of that great popular maths buzzword "chaos"...

Tonight in MS.03 El Presidente- Jamie Sawyer will explain the whole kerboodle in another one of our rather fab informal discussion thingies- anyone from any level is welcome- expect banter, dynamics and a trip to the grad.


Submitted by Newtonswig on 12 November 2007 - 2:09am.