Related papers: Limit Sets and Internal Transitivity in Free Group…
The paper gives a characterisation of the chain relation of a sofic subshift. Every sofic subshift $\Sigma$ can be described by a labelled graph $G$. Factorising $G$ in a suitable way we obtain the graph $G/_\approx$ that offers insight…
In this paper, we discuss some well-known results and some open problems of the theory of $\sigma$-properties of a group related to the study of generalized $T$-groups.
Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
Random walks cannot, in general, be pushed forward by quasi-isometries. Tame Markov chains were introduced as a `quasi-isometry invariant' are a generalization of random walks. In this paper, we construct several examples of tame Markov…
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…
When assessing group solvency, an important question is to what extent intragroup transfers may be considered, as this determines to which extent diversification can be achieved. We suggest a framework to describe the families of admissible…
We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an…
We study properties of !-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the omega-limit set of a trajectory is chain recurrent, applying this result…
It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…
We provide a simplified characterization of entanglement in physical systems which are symmetric under the action of subgroups of the symmetric group acting on the party labels. Sets of entanglements are inherently equal, lying in the same…
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
We give a topological framework for the study of Sela's limit groups: limit groups are limits of free groups in a compact space of marked groups. Many results get a natural interpretation in this setting. The class of limit groups is known…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
Let $G$ be a finite permutation group on a finite set $\Omega$. The notion of $G$ being quasi-transitive on $\Omega$ was defined by Alan Camina \cite{Camina}; in that paper conditions were established that ensured a quasi-transitive group…
Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of…
In this paper we give a concept of multi-dimensional-time dynamical system (MDTDS). Such dynamical system is generated by a finite family of functions $\{f_i\}$. The multi-dimensional-time space is taken as a free group. Using the subgroups…