Related papers: Orders of accumulation of entropy
For a continuous self-map $T$ of a compact metrizable space with finite topological entropy, the order of accumulation of entropy of $T$ is a countable ordinal that arises in the theory of entropy structure and symbolic extensions. Given…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…
In this note we present that the patch counting entropy can be obtained as a limit and investigate which sequences of compact sets are suitable to define this quantity. We furthermore present a geometric definition of patch counting entropy…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
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…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
Let $(X,\rho,G)$ be a $G-$action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
In the paper "Finite-rank Bratteli-Vershik diagrams are expansive" [DM], Downarowicz and Maass proved that the Cantor minimal system associated to a properly ordered Bratteli diagram of finite rank is either an odometer system or an…
The enumeration degrees of sets of natural numbers can be identified with the degrees of difficulty of enumerating neighborhood bases of points in a universal second-countable $T_0$-space (e.g. the $\omega$-power of the Sierpi\'nski space).…
We show that for a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) on a non-empty compact metrizable space $\Omega$, the existence of a affine space dense in the set of continuous functions on $\Omega$ constituted by elements…
This paper focuses on the extreme-value problem for Shannon entropy of the joint distribution with given marginals. It is proved that the minimum-entropy coupling must be of order-preserving, while the maximum-entropy coupling coincides…
We generalize the definition of topological entropy given by Adler, Konheim, and McAndrew (AKM) for piecewise continuous self-maps defined on a compact interval (pc-maps). For this notion of entropy, we prove that the properties of the…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…