Related papers: $n$-valued Coset Groups and Dynamics
A concise and elementary derivation of the complete asymptotic expansion for the factorial function $n!$ is presented. This treatment produces a new expression for the coefficients, and it brings to light the simple relationship between the…
The cusped hyperbolic n-orbifolds of minimal volume are well known for $n \leq 9$. Their fundamental groups are related to the Coxeter n-simplex groups $\Gamma_n$ listed in Table 1. In this work, we prove that $\Gamma_n$ has minimal growth…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well known methods available for uniformly hyperbolic systems.
We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric…
We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet derivative and super commutator, can be carried out in the…
We prove an asymptotic formula for the number of $n$-dimensional representations of the group $\mathrm{SU}(3)$. Main tools for the proof are Wright's Circle Method and the Saddle Point Method.
A novel method of asymptotic factorization of $n \times n$ matrix functions is proposed. Considered class of matrices is motivated by certain problems originated in the elasticity theory. An example is constructed to illustrate…
The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.
For classical groups SL(n), SO(n) and Sp(2n), we define uniformly geometric valuations on the corresponding complete flag varieties. The valuation in every type comes from a natural coordinate system on the open Schubert cell and is…
We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive…
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in…
We present a survey of results on profinite semigroups and their link with symbolic dynamics. We develop a series of results, mostly due to Almeida and Costa and we also include some original results on the Sch\"utzenberger groups…
In this article we relate word and subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the nilpotency of a finitely generated group…
We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.
We study the asymptotic behavior of two statistics defined on the symmetric group S_n when n tends to infinity: the number of elements of S_n having k records, and the number of elements of S_n for which the sum of the positions of their…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…
We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view to addressing, in particular, the…