Related papers: On minimal actions of countable groups

A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f:X->Y. In the case of spin systems X is a set of spin carriers and Y contains 2s+1 z-components -s<=m<=s…

We study dynamics of a substitution subshift given by the substitution a->aca, b->d, c->b, d->c that is related to the Grigorchuk group. This dynamical system is shown to be, up to a countable set, conjugated to the binary odometer.

We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [7]. We also bound the number of generic measures such a subshift can support based on its…

We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $\mu_{min}(L \otimes M) = \mu_{min}(L)\mu_{min}(M)$ for all Euclidean lattices $L$ and $M$. We prove that this is the…

We construct an explicit algebraic example of a subshift of finite type over a group $\Gamma$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…

A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincar\'e invariance, cluster separability, and the spectral condition. Irreducible representations and…

In this paper, we pay attention to a weaker version of Walters's question on the existence of non-uniform cocycles for uniquely ergodic minimal dynamical systems on non-degenerate connected spaces. We will classify such dynamical systems…

In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, defined as finite groups of particles having an influence on each other's trajectory during a given interval of…

We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for…

Let $G$ be an amenable discrete countable infinite group, $A$ a finite set, and $(\mu_g)_{g\in G}$ a family of probability measures on $A$ such that $\inf_{g\in G}\min_{a\in A}\mu_g(a)>0$. It is shown (among other results) that if the…

We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…

We consider two types of dynamical systems namely non-autonomous discrete dynamical systems(NDDS) and generic dynamical systems(GDS). In both of them, we study various notions of transitivity. We give many equivalent conditions for each of…

We investigate $\mathbb{R}^n$ as the additive group with the Euclidean topology to give a description of $S(\mathbb{R}^n)$, the phase space of the universal ambit of $\mathbb{R}^n$ and $M(\mathbb{R}^n)$, the phase space of the universal…

This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…

We consider the global minimization of a particular type of minimum structured optimization problems wherein the variables must belong to some basic set, the feasible domain is described by the intersection of a large number of functional…

We say that a countable discrete group $G$ is {\em almost Ornstein} if for every pair of standard non-two-atom probability spaces $(K,\kappa), (L,\lambda)$ with the same Shannon entropy, the Bernoulli shifts $G \cc (K^G,\kappa^G)$ and $G…

The conjecture that $N=2$ minimal models in two dimensions are critical points of a super-renormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary…

The richness of quantum theory's reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory's reversible dynamics, its local state space and the degree of non-locality…