pikenber

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# Assignment on super-attracting parameters

mark

Remember the following theorem:

A periodic orbit is super-attracting iff it contains a critical point.

Now, consider that last line of code:

```
F(c,0).roots(ring=RR)
```

Mathematically, that finds the real solutions of f_c^5(0) = 0, which should be the values of c where 0 maps back to itself after five iterates. The reason we cared about zero in the sample code for the quadratic family f_c(x)=x^2+c is because it’s the critical point. but zero is *not* the critical point of your family. Once you have your critical point (say x_0), you should solve f_c^5(x_0)=x_0 using code like

```
(F(c,x0)-x0).roots(ring=RR)
```

One other point: I think I should have asked you to use the parameter of *smallest absolute value* in your cobweb plot.