相关论文: Multidimensional effective S-adic systems are sofi…

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

A two dimensional string effective action is obtained by dimensionally reducing the bosonic part of the ten dimensional heterotic string effective action. It is shown that this effective action, with a few restrictions on some backgrounds…

In this paper, we explore the construction and dynamical properties of $\mathcal{S}$-limited shifts. An $S$-limited shift is a subshift defined on a finite alphabet $\mathcal{A} = \{1, \ldots,p\}$ by a set $\mathcal{S} = \{S_1, \ldots,…

An avoshift is a subshift where for each set $C$ from a suitable family of subsets of the shift group, the set of all possible valid extensions of a globally valid pattern on $C$ to the identity element is determined by a bounded…

We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples in two dimensions and an example in three dimensions that…

We show that in the category of effective $Z$ dynamical systems there is a universal system, i.e. one that factors onto every other effective system. In particular, for d $\geq 3$ there exist d-dimensional shifts of finite type which are…

In this work we study the entropies of subsystems of shifts of finite type (SFTs) and sofic shifts on countable amenable groups. We prove that for any countable amenable group $G$, if $X$ is a $G$-SFT with positive topological entropy $h(X)…

An idea that became unavoidable to study zero entropy symbolic dynamics is that the dynamical properties of a system induce in it a combinatorial structure. An old problem addressing this intuition is finding a structure theorem for…

The study of subshifts on groups different from $\mathbb{Z}$, such as $\mathbb{Z}^d$, $d\geq 2$, has been a subject of intense research in recent years. These investigations have unveiled aremarkable connection between dynamics and…

The main purpose of this paper is to strengthen our understanding of sofic mean dimension of two typical classes of sofic group actions. First, we study finite group actions. We prove that sofic mean dimension of any amenable group action…

We show that the image of a subshift $X$ under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of finite type, resp. a sofic subshift, if and only if so is…

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…

In this article, we study classes of multidimensional subshifts defined by multihead finite automata, in particular the hierarchy of classes of subshifts defined as the number of heads grows. The hierarchy collapses on the third level,…

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

Using a deterministic version of the self-similar (or hierarchical, or fixed-point ) method for constructing 2-dimensional subshifts of finite type (SFTs), we construct aperiodic 2D SFTs with a unique direction of non-expansiveness and…

In this paper we use fixed point tilings to answer a question posed by Michael Hochman and show that every one-dimensional effectively closed subshift can be implemented by a local rule in two dimensions. The proof uses the fixed-point…

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global…

Based on previous work of the authors, to any $S$-adic development of a subshift $X$ a "directive sequence" of commutative diagrams is associated, which consists at every level $n \geq 0$ of the measure cone and the letter frequency cone of…

We introduce the class of strongly sofic monoids. This class of monoids strictly contains the class of sofic groups and is a proper subclass of the class of sofic monoids. We define and investigate sofic topological entropy for actions of…