An undecidable problem in dynamics
Jason Bell
Abstract
Given a variety X with a self-map ϕ and subvarieties Y and Z of X, we consider the set of n for which ϕn(Y) intersects Z nontrivially. Extending a beautiful construction of Lee and Nam, we show this gives rise to an undecidable problem for a fixed ambient variety X and morphism ϕ. We further use this construction to give a counterexample to a conjecture of the author, Satriano, and Sierra.
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