How can i use the Solve function to find the actual equation for a

[peter.a]

How can i use the Solve function to find the actual equation for a fixed point?
For the function f(x)=ur(1-u)

 

[Hepth]

f[u_] := u r (1 - u)
Solve[f[f] == u, u]

the u_ means to use it as an input variable, the " := " means not to evaluate it until its used. So i just nested it once, f[f] == u should be the equation for a fixed point of f.
Solve[EQUATION,VARIABLE] is its use.

or SOLVE[{EQ1,EQ2},{V1,V2}] for multivariate solutions.

I assume "u" was the variable in this case as f(x) = u r (1- u) has no x in it.

 

[peter.a]

why have you done f[f==u and not f==u?
is this because then it also gives the complex solutions?

 

[Hepth]

Ah that was a mistake. I was thinking of attractive fixed point functions.

Yeah Solve[f==u,u] should be enough. It will give all solutions, include any complex ones.

 

[peter.a]

Thanks for clearing that up, because i was getting confused