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Let ${\Phi }^{\lambda }$ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for ${\Phi }^{\lambda }$ for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for ${\Phi }^{\lambda }$, then we show that for each λ ∈ K̅, a(λ) is torsion for ${\Phi }^{\lambda }$ if and only if b(λ) is torsion for ${\Phi }^{\lambda }$. In the case a,b ∈ K, we prove in addition that a and b must be ${̅}_p$-linearly dependent.

Let $\varphi :X\to X$ be a morphism of a variety defined over a number field $K$, let $V\subset X$ be a $K$-subvariety, and let ${𝒪}_{\varphi }\left(P\right)=\{{\varphi }^n\left(P\right):n\ge 0\}$ be the orbit of a point $P\in X\left(K\right)$. We describe a local-global principle for the intersection $V\cap {𝒪}_{\varphi }\left(P\right)$. This principle may be viewed as a dynamical analog of the Brauer–Manin obstruction. We show that the rational points of $V\left(K\right)$ are Brauer–Manin unobstructed for power maps on ${\mathbb{P}}^2$ in two cases: (1) $V$ is a translate of a torus. (2) $V$ is a line and $P$ has a preperiodic coordinate. A key tool in the proofs is the classical...