Related papers: Periodicity and Dynamical Systems of Dickson Polyn…

The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…

This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…

We consider the dynamical system created by iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. We study the primitive period of a periodic point in this field in relation to the…

We introduce a notion of strong periodicity of a module over a finite-dimensional algebra over a field. We prove that the existence of such modules over certain idempotent algebras is both a necessary and sufficient condition for the…

For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by $\nu_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations $\nu_{p}(Q(n))$ is shown to be either periodic or unbounded. The first…

We complete the study of some periods of polynomials in (n+1) variables with (n+2) monomials in computing the behavior of these periods in the natural parameter for such a polynomial.

Let $\mathbb{F}_q$ be the finite field with $q=p^s$ elements, where $p$ is an odd prime and $s$ a positive integer. In this paper, we define the function $f(X)=(cX^q+aX)(X^{q}-X)^{n-1}$, for $a,c\in\mathbb{F}_q$ and $n\geq 1$. We study the…

We study the discrete dynamics of standard (or left) polynomials $f(x)$ over division rings $D$. We define their fixed points to be the points $\lambda \in D$ for which $f^{\circ n}(\lambda)=\lambda$ for any $n \in \mathbb{N}$, where…

An n dimensional monomial dynamical system over a finite field K is a nonlinear deterministic time discrete dynamical system with the property that each of the n component functions is a monic nonzero monomial function in n variables. In…

The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…

Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)),…

The aim of our paper is to formulate and solve problems concerning linear multiple periodic recurrence equations. Among other things, we discuss in detail the cases with periodic and multi-periodic coefficients, highlighting in particular…

We study orbits and fixed points of polynomials in a general skew polynomial ring $D[x,\sigma, \delta]$. We extend results of the first author and Vishkautsan on polynomial dynamics in $D[x]$. In particular, we show that if $a \in D$ and $f…

Polynomially-recursive sequences generally have a periodic behavior mod $m$. In this paper, we analyze the period mod $m$ of a second order polynomially-recursive sequence. The problem originally comes from an enumeration of avoiding…

The article deals with a lexicographic order in various sequences. Consider the axiomatic of lexicographic series, based on the properties of the natural numbers. Elements of the set are ordered first the code length; further in each sign…

We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…

Let $\mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with…

The purpose of this note is to characterize those orthogonal polynomials sequences $(P_n)_{n\geq0}$ for which $$ \pi(x)\mathcal{D}_q P_n(x)=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0,1,2,\dots, $$ where $\mathcal{D}_q$ is the Askey-Wilson…

We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{F}_p$. We also study the permutation…

We study the periodical solutions of a Poisson-gradient PDEs system with bounded nonlinearity. Section 1 introduces the basic spaces and functionals. Section 2 studies the weak differential of a function and establishes an inequality.…