1: Visit to IT
3: Inf Dim
1: So, I went to IT on Friday to see if they could help me with accessing GAIO remotely from my laptop. After I told them my problem, all I got (from everyone I talked to) was "Oh, the math department. Well, they got their own thing going on, so I don't know." And then they told me it would just probably be better to go to the lab to do my work. They did give me the name of someone in the math dept I can maybe talk to (I'm looking for where I wrote it down...). I also tried accessing it with XWin because I think that's how Prof Li was able to access it from his PC, but I can't figure out how to work it. So, for now, still doing GAIO from the lab.
2: I did do some work on Matlab today. I got some nice graphs (that I can't access right now since I can't access the lab, but I'll put up tomorrow). I've got a few ideas of things I can try tomorrow with local dimension. I tried using the "function" function with solve to find periodic points (so I could maybe find other points on the attractor) but it didn't work.
3: I'm not really sure what I should be doing with infinite dimensions. I found this book (Infinite Dimensional Dynamical Systems in Mechanics and Physics, by Roger Temam) that looks like it might be about the things I'm doing, but I'm not sure if I should go through and read/learn the stuff since it's very similar to what Prof Day told me I should be doing myself (dimensions of attractors, fractal (box counting) dimension in infinite dimensions). It all looks really complicated though, and I'm pretty sure I wouldn't be able to derive it all myself anyway.
Also, with the topology: I don't see how changing the topology of a set is going to change the box counting dimension. I'm pretty sure you can use open sets, closed sets or neither for your box as long as it's connected (maybe) and bounded with length equal to epsilon and epsilon going to zero. The impression I get from Hausdorff is that it is almost the same except that the "boxes" are less than or equal to epsilon with epsilon going to zero (sort of). That's why Haus = Box for regular Cantor Sets, since the epsilons are all equal.