Related papers: Mixing properties in coded systems

We study topological mixing properties and the maximal equicontinuous factor of rank-one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank-one subshift is finite. We also determine all the…

Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the…

Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…

Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they…

We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…

We show that systems with some specification properties are topologically or almost Borel universal, in the sense that any aperiodic subshift with lower entropy may be topologically or almost Borel embedded.

We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…

We show that a topological dynamical system is either minimal or have positive topological entropy. Moreover, for equicontinuous systems, we show that topological transitivity, minimality and orbit gluing property are equivalent. These…

A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity of weak mixing transformations.…

Let $(X, T)$ be a weakly mixing minimal system, $p_1, \cdots, p_d$ be integer-valued generalized polynomials and $(p_1,p_2,\cdots,p_d)$ be non-degenerate. Then there exists a residual subset $X_0$ of $X$ such that for all $x\in X_0$ $$\{…

We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.

This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…

We show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing.

This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…

In this note we complete the analysis carried on in \cite{CGSV} about the topological synchronisation of unimodal maps of the interval coupled in a master-slave configuration, by answering to the questions raised in that paper. Namely, we…

In this paper, we introduce a standard generator matrix for mixed-alphabet linear codes over finite chain rings. Furthermore, we show that, when one has a linear complementary pair (LCP) of mixed-alphabet linear codes, both codes are…

The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes.…

Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…

We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences…