Let $P$ be a polynomial in complex variable $z$ of degree $d$
i.e. $P(z)= a_d z^d+.....+a_1 z+a_0$
Now I want to calculate following limit
$f(z) = \limsup_{n \to \infty} \frac{1}{d^n} (Log|P(z)^{*n} - b|)$
where $b \in$$\mathbb C$ is constant and $P(z)^{*n}$ is $n$ times composition of $P$.
I tried to take roots of $P^{*n}$ under $b$ and then root decomposition but couldn’t succeed. Any hint is welcome.