Reduction of polynomial dynamical systems modulo primes
Sudhansu Sekhar Rout
TL;DR
This paper investigates the behavior of polynomial dynamical systems modulo primes, focusing on height growth, periodic points, and orbit intersections over finite fields, providing new insights into their algebraic and arithmetic properties.
Contribution
It introduces new estimates for height growth and analyzes periodic points and orbit intersections of polynomial systems over finite fields.
Findings
Height growth of iterations is bounded under certain conditions.
Periodic points over finite fields are characterized using reduction modulo primes.
Orbit intersections are analyzed with new algebraic methods.
Abstract
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of multivariate polynomials over the integers, we study the periodic points and the intersection of orbits of such dynamical systems over finite fields. 1
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Mathematical Dynamics and Fractals