Related papers: Multidimensional effective S-adic systems are sofi…
In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
We give a sufficient geometric condition for a subshift to be measurably isomorphic to a domain exchange and to a translation on a torus. And for an irreducible unit Pisot substitution, we introduce a new topology on the discrete line and…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
We provide an example of a non-finitely generated group which admits a nonempty strongly aperiodic SFT. Furthermore, we completely characterize the groups with this property in terms of their finitely generated subgroups and the roots of…
Given sofic approximations for countable, discrete groups $G,H$, we construct a sofic approximation for their wreath product $G\wr H$.
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Decision making is a fundamental capability of autonomous systems. As decision making is a process which happens over time, it can be well modeled by dynamical systems. Often, decisions are made on the basis of perceived values of the…
In this paper we prove that the two dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion. There are six general fundamental classes of…
We examine several definitions of soficity for monoids obtained by generalizing various definitions of sofic groups. They are not all equivalent and include the definition recently introduced by Ceccherini-Silberstein and Coornaert. One of…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…
In this paper we show that an instance of dividing in pseudofinite structures can be witnessed by a drop of the pseudofinite dimension. As an application of this result we give new proofs of known results for asymptotic classes of finite…
We show that all rank-one transformations are subsequence boundedly rationally ergodic and that there exist rank-one transformations that are not weakly rationally ergodic.
In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential…
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic measures with finite moments. The main technical tool is duality combined with successful coupling.
In the paper, we describe all total orders $\succ$ compatible with addition on additive subsemigroup $S$ of finite dimensional spaces over rational numbers. We provide a necessary and sufficient condition under which a finitely generated…
In this paper, we shall prove that all actions of LERF groups on sets are sofic. As a corollary, we obtain that a large class of generalized wreath products are sofic.