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Iskovskikh Seminar
September 25, 2014 18:00, Moscow, Steklov Mathematical Institute, room 540

The dynamical Mordell–Lang problem

E. Gorinov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The talk is based on works of J.P.Bell, D.Ghioca, and T.J.Tucker. Let $x \in X$ be a point in a Noetherian space, let $f:X \rightarrow X$ be a continuous function, and let $Y \subset X$ be a closed set. We show that the set $S := {n \in \mathbb{N}: f^n(x) \in Y}$ is a union of finitely many arithmetic progressions and a set with Banach density zero. We also discuss some corollaries of this result.