Current trends and open problems in arithmetic dynamics

R Benedetto, P Ingram, R Jones, M Manes… - Bulletin of the American …, 2019 - ams.org
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A
relatively new field, it draws inspiration partly from dynamical analogues of theorems and …

[LIBRO][B] The Dynamical Mordell–Lang Conjecture

JP Bell, D Ghioca, TJ Tucker - 2016 - books.google.com
The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang
conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point …

On multiplicatively dependent vectors of algebraic numbers

F Pappalardi, M Sha, I Shparlinski, C Stewart - Transactions of the …, 2018 - ams.org
On multiplicatively dependent vectors of algebraic numbers Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 370, Number 9, September 2018, Pages …

Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems

C D'Andrea, A Ostafe, I Shparlinski… - Transactions of the …, 2019 - ams.org
We give bounds for the number and the size of the primes $ p $ such that a reduction
modulo $ p $ of a system of multivariate polynomials over the integers with a finite number …

Solutions to multiplicative Diophantine equations in orthotopes

M Afifurrahman, CC Corrigan - arxiv preprint arxiv:2501.15372, 2025 - arxiv.org
In this article, we study the number of solutions of bounded height to certain multiplicative
Diophantine equations. We provide a framework on counting the number of integer solutions …

Orbits of algebraic dynamical systems in subgroups and subfields

A Ostafe, IE Shparlinski - … and Applications: Festschrift in Honour of Robert …, 2017 - Springer
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The orbit intersection problem in positive characteristic

SS Rout - arxiv preprint arxiv:2102.04073, 2021 - arxiv.org
In this paper, we study the orbit intersection problem for the linear space and the algebraic
group in positive characteristic. Let $ K $ be an algebraically closed field of positive …

Unlikely intersections over finite fields: polynomial orbits in small subgroups

L Mérai, IE Shparlinski - arxiv preprint arxiv:1904.12621, 2019 - arxiv.org
We estimate the frequency of polynomial iterations which falls in a given multiplicative
subgroup of a finite field of $ p $ elements. We also give a lower bound on the size of the …

[HTML][HTML] The dynamical Mordell-Lang problem for intersection of two orbits

SS Rout - Journal of Number Theory, 2020 - Elsevier
Let X be an algebraic variety defined over C, let α∈ X (C) and Φ: X⟶ X be a morphism. The
Dynamical Mordell-Lang conjecture describes the intersection of an orbit Orb Φ (α) with a …

On intersections of polynomial semigroups orbits with plane lines

J Mello - Canadian Mathematical Bulletin, 2021 - cambridge.org
On intersections of polynomial semigroups orbits with plane lines Page 1 Canad. Math. Bull.
Vol. 64 (2), 2021, pp. 442–451 http://dx.doi.org/10.4153/S0008439520000557 © Canadian …