I'm seeking a solution (if one is known to exist) to the following recurrence relation:
$x_{t+1}^2 = ax_t+bx_t^2$.
where $a\in(0,1)$, $b\in(0,1)$. I know $x_0\in(1,3)$, but its value varies case-by-case within that range. Ideally the solution would be of the form $x_t = f(x_0,a,b,t)$.
Any help solving this? Is there hope? Thanks in advance!
John