iteration of fractional linear functions

[bo198214]

quite interesting; though it didn't come to my attention when I fiddled a bit with functions like this.

I found it again. Its your post about iteration of 1/(x+1). You dont mention the sci.math thread explicitely, but I think I had a look it at it at that time and thatswhy remembering that some people had quite a knowledge about iteration of fractional linear maps. May be I read Alain there.

You asked in your thread about different methods of iterating 1/(x+1). This is a particular case of iterating a fractional linear map.
Kinda this thread is a generalization of your problem.
I see the 3 methods: regular iteration at the first fixed point, regular iteration at the second fixed point, and fractional iteration of the characteristic 2x2 matrix.

In your web-page you do regular iteration at one fixed point (via your matrix method). But it is not clear to me whether you compare the result with the regular iteration at the other fixed point.