Related papers: A variational principle for entropy of a random dy…

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…

In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a…

In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

We consider topological dynamical systems given by skew products $S\rtimes_{\tau} T$, where $S\colon Y\to Y$ is a subshift, $\tau\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For…

We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…

We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…

We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In…

Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…

Let $(X,G)$ be a $G$-action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version…

Let $(X,T)$ be a topological dynamical system. We define the measure-theoretical lower and upper entropies $\underline{h}_\mu(T)$, $\bar{h}_\mu(T)$ for any $\mu\in M(X)$, where $M(X)$ denotes the collection of all Borel probability measures…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

We consider actions of a tileable amenable group $\Gamma$ on a topological space $X$. For a continuous function on $X$, we define the entropy of the number of homologically detectable critical point of the average of that function over…

In this paper, we introduce a concept of nonlinear local topological pressure defined via open covers and establish a corresponding variational principle. Furthermore, we provide multiple equivalent characterizations of nonlinear pressure…