This book is designed to provide a path for the reader into an amalgamation oftwo venerable
areas ofmathematics, Dynamical Systems and Number Theory. Many of the motivating …

This book provides an overview of the theory of p-adic (and more general non-
Archimedean) dynamical systems. The main part of the book is devoted to discrete …

Abstract Let φ: P^ N_K → P^ N_K be a morphism of degree d≥ 2 defined over a field K that
is algebraically closed field and complete with respect to a nonarchimedean absolute value …

In this paper we study the monomial dynamical systems of dimension one over finite fields
from the viewpoints of arithmetic and graph theory. We give formulas for the number of …

In this thesis we investigate monomial dynamical systems over the fields of p-adic numbers,
Qp, or over finite field extensions of them. A finite extension of Qp is denoted by Kp. The …

Let Prºf (a) be the polynomial whose zeros are the r-periodic points of the polynomial f (a) e
Z [a]. We will show that if Prºf (a) is separable over Q, then the average of numbers of linear …

We obtain some results about the repeated exponentiation modulo a prime power from the
viewpoint of arithmetic dynamical systems. In particular, we extend two asymptotic formulas …

Let A (n, a, y) denote a specific weighted average of different zeros of fn (x)− x for all prime
numbers p≤ y, where f (x)= xp+ ax∈ Fp [x], a= 0, and fn denotes the n-fold composition of f …

Discrete dynamical systems of the kind g (a)= a+ f (a), where f (a) is a monic irreducible
polynomial of prime degree with coefficients in Zp, will be investigated. The fixed points of …

Dynamical systems in unramified or totally ramified extensions of a p-adic field Page 1
Izvestiya: Mathematics Dynamical systems in unramified or totally ramified extensions of a -adic …