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Related papers: A Note on Entropy of Delone Sets

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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…

Dynamical Systems · Mathematics 2013-06-21 Anthony H. Dooley , Guohua Zhang

We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…

Dynamical Systems · Mathematics 2018-06-05 Jose F. Alves , Antonio Pumarino

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…

Dynamical Systems · Mathematics 2007-05-23 Boris Hasselblatt , Zbigniew Nitecki , James Propp

We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is…

Functional Analysis · Mathematics 2020-04-22 Dorothee D. Haroske , Leszek Skrzypczak

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to…

Commutative Algebra · Mathematics 2018-10-15 Mahdi Majidi-Zolbanin , Nikita Miasnikov

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…

Dynamical Systems · Mathematics 2023-03-27 Xiankun Ren , Xueting Tian , Yunhua zhou

In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…

Dynamical Systems · Mathematics 2024-10-29 Maysam Maysami Sadr , Mina Shahrestani

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

Group Theory · Mathematics 2020-01-09 Anna Giordano Bruno , Flavio Salizzoni

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where…

Discrete Mathematics · Computer Science 2007-11-14 Aoi Honda , Michel Grabisch

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…

Statistical Mechanics · Physics 2009-11-11 Israel Klich , Gil Refael , Alessandro Silva

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…

Dynamical Systems · Mathematics 2018-06-26 Tobias Jäger , Daniel Lenz , Christian Oertel

In this paper we study the capacity/entropy region of finite, directed, acyclic, multiple-sources, multiple-sinks network by means of group theory and entropy vectors coming from groups. There is a one-to-one correspondence between the…

Information Theory · Computer Science 2013-08-12 Pirita Paajanen

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…

Dynamical Systems · Mathematics 2021-09-20 Shilpak Banerjee , Philipp Kunde , Daren Wei

A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering…

Dynamical Systems · Mathematics 2024-10-11 Daniel Gonçalves , Danilo Royer , Felipe Augusto Tasca

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…

Symplectic Geometry · Mathematics 2007-05-23 Urs Frauenfelder , Felix Schlenk

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…

Dynamical Systems · Mathematics 2023-03-15 Gabriel Fuhrmann , Maik Gröger , Tobias Jäger , Dominik Kwietniak

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…

Dynamical Systems · Mathematics 2021-08-30 Sebastián Barbieri , Felipe García-Ramos

Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…

Dynamical Systems · Mathematics 2017-08-03 Christoph Kawan

This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is…

Dynamical Systems · Mathematics 2007-05-23 Jeffery C. Lagarias , Peter A. B. Pleasants

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…

Dynamical Systems · Mathematics 2023-11-07 Lewis Bowen