The average number of integral points in orbits
The average number of integral points in orbits
Over a number field $K$, a celebrated result of Silverman states that if $\varphi(z)\in K(z)$ is a rational function whose second iterate is not a polynomial, the set of $S$-integral points in the orbit $\text{Orb}_\varphi(P)=\{\varphi^n(P)\}_{n\geq0}$ is finite for all $P\in \mathbb{P}^1(K)$. In this paper, we show that if we vary …