04/23/2009, 08:39 AM

andydude Wrote:According to Markus Müller, the superfunction of from (-1) is .

Is that right? can I say "from"?

If you mean the fixed point then I would say "at". However -1 is not a fixed point of but 1 is, so I dont know exactly what you mean.

Yes is a superfunction of .

Is it regular?

The regular iteration is characterized by being differentiable (but at least asymptotically differentiable) at the fixed point . (This also implies that .)

The iteration is given in terms of the superfunction by:

has two fixed points 1 and :

is not invertible at 1, but it is invertable at .

So the t-th iterate of is differentiable at and so is the regular superfunction at .