Related papers: Counting dynamical systems over finite fields
We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
Let $q\geqslant 2$ be a fixed prime power. We prove an asymptotic formula for counting the number of monic polynomials that are of degree $n$ and have exactly $k$ irreducible factors over the finite field $\mathbb{F}_q$. We also compare our…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The…
We consider dynamical systems with boundary control associated with finite Jacobi matrices. Using the method previously developed by the authors, we associate with these systems special Hilbert spaces of analytic functions (de Branges…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…
Some linear dynamical systems over finite fields are studied and the self-similar character of their development is proved. Connections with aperiodic tilings, Delanoy numbers and other topics are also proved. The prime fields F_p have a…
In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties. As an…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…