06/22/2009, 02:24 PM

(06/22/2009, 12:37 AM)Tetratophile Wrote: and added "f has no other fixed points", because I thought other fixed points would mess things up.Well, but *has* more fixed points. In every strip there is a fixed point of .

Quote:(3) We can repeat (4.2) as many times as needed to get to .

No, we can not.

1. The curve may get out of the strip of bijectivity of what indeed happens for . (plot the curves!)

2. may hit , i.e. the extension of overlaps with the original domain. If meets at an angle then meets at an angle . So the image curves rotate around L. This includes also the comment of Ben, that if , i.e. if is real, then then the images do not rotate, and hence one would never reach if it hits in a different angle.