mark

Let $f(x)=3 x^2-6 x+3.415$. Find all attractive orbits of $f$.

An archived instance of discourse for discussion in undergraduate Complex Dynamics.

mark

Let $f(x)=3 x^2-6 x+3.415$. Find all attractive orbits of $f$.

Rick

To find super attractive orbits of f, we must find where $F'(x)=0$ where $F=f^n$.

So, if $F(x)=3x^2−6x+3.415$ then $F'(x)=6x-6=0$ and $x=1$.

Therefore, $x=1$ and it's orbit are super attractive.

mark

@Rick I think you're on the right track and starting at $x=1$ is the right idea. An orbit, however, consists of more than one point. Also, I mistakenly wrote *super*-attractive originally when I meant only *attractive*. That's my bad but definitely an important distinction.