08/11/2009, 03:52 PM

(08/11/2009, 03:42 PM)bo198214 Wrote: No, I dont follow your line of thoughts. Somehow you assume that one of both is the perfect iteration while the other is the bad one with sinoidal deviation, dont you?Well, that was a hypothesis from where I was thinking: it may well be, that a function developed at an attracting fixpoint behaves different from one with a repelling one. But I'm (hopefully) not fixed to such hypotheses...

Quote:Imho both have the same right to live (though only the lower fixed point is usable for a tetrational). Each of them is holomorphic at its fixed point while non-holomorphic at the other fixed point.... which is a good argument...

Quote:I guess with matrix power iteration along the points p in the interval [2,4] we can smoothly deform the tet[p=2] into tet[p=4], where tet[p] is always a superfunction/iteration that though will neither be holomorphic at any of both fixed points.Yepp, as I said in my other post: I'll just find it interesting to quantify the difference and possibly have a functional expression for it. (The same problem which I had with the alternating iteration-series ("tetra-series" as I called them then))

Remember that matrix power iteration coincides with regular iteration when applied to fixed points.

The oscillating behaviour is not contained in the "bad" tetrational but born through taking the difference. *Both* contribute to the oscillation.

The behaviour must be oscillating as we know that f^{-1}(g(z)) - z is 1-periodic.

Gottfried Helms, Kassel