08/12/2022, 02:14 AM
(08/09/2022, 12:07 PM)bo198214 Wrote: Ok, I even can give a polynomial
\[ p (x) = x ^ 3 + \frac{\sqrt{5}-3}{2} x^2 - \frac{\sqrt{5}-3}{2} x \]
has fixed points 0 and 1 and
\[ p'(x) = 3x^2 + (\sqrt{5}-3)x - \frac{\sqrt{5}-3}{2} \]
The derivatives at the fixed points are:
\( p'(0) = -\frac{\sqrt{5}-3}{2}, p'(1) = 3 + \frac{\sqrt{5}-3}{2}=\frac{\sqrt{5}+3}{2}\) hence
\[ p'(0)p'(1) = -\frac{(\sqrt{5}-3)(\sqrt{5}+3)}{4} = 1\]
you got the fixpoints derivatives connection right.
but how do you know both regulars agree ?
