S-integral preperiodic points for dynamical systems over number fields

Given a rational map $ϕ: {\mathbb P}^1\to {\mathbb P}^1$ defined over a number field $K$, we prove a finiteness result for $ϕ$-preperiodic points which are $S$-integral with respect to a non-preperiodic point $P$, provided $P$ satisfies a certain local condition at each place. This verifies a special case of a conjecture of S. Ih.

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