Related papers: $n$-valued Coset Groups and Dynamics
This article answers the question of V.M. Buchstaber about the growth function of a particular $n$-valued group. This question is closely related to discrete integrable systems. In this paper, we will find a formula for the growth function…
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we…
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
The rich theory of Coxeter groups is used to provide an algebraic construction of finite volume hyperbolic n-manifolds. Combinatorial properties of finite images of these groups can be used to compute the volumes of the resulting manifolds.…
We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…
The principal aim of this article is to introduce and study n-valued quandles and n-corack bialgebras. We elaborate the basic methods of this theory, reproduce the coset construction known in the theory of n-valued groups. We also consider…
We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.
In this survey we will present the symbolic extension theory in topological dynamics, which was built over the past twenty years.
We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroup is infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics…
This paper gives asymptotic formulas for the subgroup growth and maximal subgroup growth of all Baumslag-Solitar groups.
We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…
We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.
We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…
We investigate the rate of growth of the function of n which counts the number of complex irreducible representations of a fixed group of degree less than or equal to n. The emphasis is on linear groups, especially compact real and p-adic…
The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…
It is relatively easy to construct a finitely generated group with infinite asymptotic dimension: the restricted wreath product of $\mathbb{Z}$ by $\mathbb{Z}$ provides an example. In light of this, it becomes interesting to consider the…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…