On the distribution of orbits in affine varieties Public Deposited

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  • Given an affine variety X, a morphism ϕ:X→X, a point α∈X, and a Zariski-closed subset V of X, we show that the forward ϕ-orbit of α meets V in at most finitely many infinite arithmetic progressions, and the remaining points lie in a set of Banach density zero. This may be viewed as a weak asymptotic version of the dynamical Mordell–Lang conjecture for affine varieties. The results hold in arbitrary characteristic, and the proof uses methods of ergodic theory applied to compact Berkovich spaces.
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  • Petsche, C. (2015). On the distribution of orbits in affine varieties. Ergodic Theory and Dynamical Systems, 35(07), 2231-2241. doi:10.1017/etds.2014.26
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