Related papers: A Study of Directional Entropy Arising from \(\mat…

In this paper we study the measure-theoretical entropy of the one-dimensional linear cellular automata (CA hereafter) $T_{f[-l,r]}$, generated by local rule $f(x_{-l},...,x_{r})= \sum\limits_{i=-l}^{r}\lambda_{i}x_{i}(\text{mod}\ m)$, where…

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between…

We analytically determine the dynamical properties of two dimensional field driven Lorentz gases within the thermodynamic formalism. For dilute gases subjected to an iso-kinetic thermostat, we calculate the topological pressure as a…

We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…

In this paper we introduce the definition of entropy for a partial $\mathbb{Z}$-action. We show that the definition of partial entropy is an extension of the definition of topological entropy for a $\mathbb Z$-action. We also prove that the…

This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…

We show that for every linear toral automorphism, especially the non-hyperbolic ones, the entropies of ergodic measures form a dense set on the interval from zero to the topological entropy.

If M is a monoid (e.g. the lattice Z^D), and G is a finite (nonabelian) group, then G^M is a compact group; a `multiplicative cellular automaton' (MCA) is a continuous transformation F:G^M-->G^M which commutes with all shift maps, and where…

Since Bandt et al. have shown that the permutation entropy and the Kolmogorov-Sinai entropy coincide for piecewise monotone interval maps, the relationship of both entropies for time-discrete dynamical systems is of a certain interest. The…

We propose a noble notion of the directional emission in microcavity lasers. First, Shannon entropy of the far-field profiles in the polar coordinate can quantify the degree of unidirectionality of the emission, while previous notions about…

Let $(M,g)$ be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on $M$. Let $\epsilon >0$. We study the semiclassical measures…

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the…

To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically…

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow…

The Ruelle thermodynamic formalism for dynamical trajectories over the large time $T$ corresponds to the large deviation theory for the information per unit time of the trajectories probabilities. The microcanonical analysis consists in…

This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number…

Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…

In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which…

We study the directional entropy of rank one Z^d actions. We show that if the sequence of towers generating the action are rectangular in shape, then there is always a direction along which the directional entropy is zero. If the rectangles…