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On constructing permutations of finite fields
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Periodic points, linearizing maps, and the dynamical Mordell–Lang problem
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The dynamical Mordell-Lang problem for étale maps
We prove a dynamical version of the Mordell-Lang conjecture for étale endomorphisms of quasiprojective varieties. We use $p$-adic methods inspired by the work of Skolem, Mahler, and Lech, combined…
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Towards a Dynamical Manin–Mumford Conjecture
We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of abelian…
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A GEOMETRIC VARIANT OF TITCHMARSH DIVISOR PROBLEM
We formulate a geometric analog of the Titchmarsh divisor problem in the context of abelian varieties. For any abelian variety A defined over ℚ, we study the asymptotic distribution of the primes of…
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Linear relations between polynomial orbits
We study the orbits of a polynomial f 2CŒX , namely, the sets 1 ;f . /; f .f . //; : : :o with 2 C. We prove that if two nonlinear complex polynomials f;g have orbits with infinite intersection, then…
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Reductions of points on elliptic curves
AbstractLet E be an elliptic curve defined over $${\mathbb{Q}}$$. Let Γ be a subgroup of rank r of the group of rational points $${E(\mathbb{Q})}$$ of E. For any prime p of good reduction, let…
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On permutation polynomials of prescribed shape
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A case of the dynamical Mordell–Lang conjecture
We prove a special case of a dynamical analogue of the classical Mordell–Lang conjecture. Specifically, let φ be a rational function with no periodic critical points other than those that are totally…
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Periods of orbits modulo primes
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