–3 PERIOD IMPLIES CHAOS!
Seemed a lot funnier in my head after 27 hours awake.
Or more like 32 hours no sleep.
Then 2 hours sleep.
Then 6 hours no sleep.
Getting really loony.
Update: I got about 10 hours sleep last night and woke up refreshed.
I’ve been up since 9AM on Sunday. I managed to sleep from 2:30PM till 5PM. I had an important exam this morning. It went well, but it’s left be a bit knackered.
I plan on staying up another half hour to complete my work and then hit the sack. Tomorrow I can sleep in, but I’ve got another exam on Thursday. I’ve cleared my schedule on Thursday, so I should be able to study hard for that exam as well. I’ve been using Red Bull on this end of semester and I have to say that it works well when used in moderation.
My exam went pretty well. Otherwise than obsessing on the Li-Yorke Theorem, I’m sure that I did pretty well, a lot better than the last exam. Li-Yorke is really useful for demonstrating that a function is chaotic. All that you need to find is a 3-periodic point. Once you have that, it implies that f is chaotic. It’s a lot easier than showing that all periodic points are dense, transitive and that f is sensitive to initial conditions.