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Related papers: Local entropy theory and applications

200 papers

We introduce a new concept of finite-time entropy which is a local version of the classical concept of metric entropy. Based on that, a finite-time version of Pesin's entropy formula and also an explicit formula of finite-time entropy for…

Dynamical Systems · Mathematics 2014-06-27 Luu Hoang Duc , Stefan Siegmund

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

General Topology · Mathematics 2020-09-08 Artur Piękosz

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

Optimization and Control · Mathematics 2016-10-14 James Schmidt

In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…

Dynamical Systems · Mathematics 2015-06-04 Hua Shao , Yuming Shi , Hao Zhu

In the study of aperiodic order via dynamical methods, topological entropy is an important concept. In this paper, parts of the theory, like Bowen's formula for fibre wise entropy or the independence of the definition from the choice of a…

Dynamical Systems · Mathematics 2020-03-10 Till Hauser

We investigate connections between local tameness of a group and a number of its ends.

Group Theory · Mathematics 2026-05-01 Rita Gitik

Each continuous action of a countably infinite discrete group $\Gamma$ on a compact metrizable space X induces a continuous action of $\Gamma$ on the space M(X) of Borel probability measures on X. We compare the local entropy theory for…

Dynamical Systems · Mathematics 2025-07-08 Hanfeng Li , Kairan Liu

By refining the method proposed in arXiv:2010.07660, entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Noether conserved charge in the Einstein gravity…

General Relativity and Quantum Cosmology · Physics 2024-07-12 Shuichi Yokoyama

This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…

Combinatorics · Mathematics 2012-07-11 Reinhard Diestel

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…

Mathematical Physics · Physics 2025-07-10 Henrik Jeldtoft Jensen , Piergiulio Tempesta

For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…

Optimization and Control · Mathematics 2022-12-13 Fritz Colonius , Boumediene Hamzi

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each…

Cellular Automata and Lattice Gases · Physics 2008-09-22 Joseph T. Lizier , Mikhail Prokopenko , Albert Y. Zomaya

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…

Dynamical Systems · Mathematics 2022-07-05 A. Arbieto , E. Rego

We will consider various definitions of topological entropy for multivalued nonautonomous dynamical systems in compact Hausdorff spaces. Some of them can deal with arbitrary multivalued maps, i.e. when no restrictions are imposed on them.…

Dynamical Systems · Mathematics 2024-06-25 Pavel Ludvík , Jan Andres

This is the monograph on the theory and applications of copula entropy (CE). This book first introduces the theory of CE, including its background, definition, theorems, properties, and estimation methods. The theoretical applications of CE…

Methodology · Statistics 2025-12-23 Jian Ma

We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures…

Dynamical Systems · Mathematics 2018-09-28 Christian Wolf , Yun Yang

We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…

General Topology · Mathematics 2014-01-16 Anna Giordano Bruno

We undertake a local analysis of combinatorial independence as it connects to topological entropy within the framework of actions of sofic groups.

Dynamical Systems · Mathematics 2013-01-08 David Kerr , Hanfeng Li

Recently, the author and collaborators proposed a method to construct a new conserved charge different from the Noether one for general relativistic field theory on curved space-time with energy-momentum tensor covariantly conserved, and…

High Energy Physics - Theory · Physics 2023-12-21 Shuichi Yokoyama

We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…

Dynamical Systems · Mathematics 2021-01-05 Ilaria Castellano , Anna Giordano Bruno