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   Articles with "measure theoretic" as a keyword



Topological r-Entropy and Measure Theoretic r-Entropy for Amenable Group Actions

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recommendations! Published in 2021 at "Journal of Dynamical and Control Systems"

DOI: 10.1007/s10883-021-09554-1

Abstract: In this paper, we introduce the concept of measure theoretic r-entropy on a compact metric space in the context of amenable group actions. To be precise, we generalize Katok’s r-entropy formula and Brin-Katok r-entropy formula… read more here.

Keywords: amenable group; group actions; measure theoretic; theoretic entropy ... See more keywords

Katok formula for the induced measure-theoretic entropy

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recommendations! Published in 2018 at "Dynamical Systems"

DOI: 10.1080/14689367.2017.1329402

Abstract: ABSTRACT Entropy is undoubtedly one of the most essential characteristics of dynamical systems. In this article, we define a topological version of the induced measure-theoretic entropy and obtain its Katok entropy formula. We show that… read more here.

Keywords: induced measure; measure theoretic; entropy; formula ... See more keywords

Measure-theoretic equicontinuity and rigidity

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recommendations! Published in 2020 at "Nonlinearity"

DOI: 10.1088/1361-6544/ab8a67

Abstract: Let $(X,T)$ be a topological dynamical system and $\mu$ be a invariant measure, we show that $(X,\mathcal{B},\mu,T)$ is rigid if and only if there exists some subsequence $A$ of $\mathbb N$ such that $(X,T)$ is… read more here.

Keywords: theoretic equicontinuity; equicontinuity rigidity; measure; measure theoretic ... See more keywords

A note on weighted measure-theoretic pressure

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recommendations! Published in 2025 at "Open Mathematics"

DOI: 10.1515/math-2024-0125

Abstract: Abstract In this article, we investigate the relations between various types of weighted measure-theoretic pressures and different versions of weighted topological pressures. We show that various types of weighted measure-theoretic pressures for an ergodic measure… read more here.

Keywords: note weighted; theoretic pressure; measure theoretic; measure ... See more keywords

Some measure-theoretic aspects of fractal functions: invariant measures and function spaces

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recommendations! Published in 2024 at "Quaestiones Mathematicae"

DOI: 10.2989/16073606.2024.2351596

Abstract: Abstract Barnsley (1986) introduced the concept of fractal interpolation functions (FIFs). Thereafter, numerous theories have been developed concerning FIFs and their properties. In this article, we explore some measure theoretic aspects of FIFs generated by… read more here.

Keywords: measure theoretic; function spaces; invariant measures; theoretic aspects ... See more keywords

A Priori Uniform Bounds as Measure-Theoretic Tools: Long-Term Analysis via Classical-Enhanced Synthesis

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recommendations! Published in 2025 at "Mathematics"

DOI: 10.3390/math13193095

Abstract: This work presents a systematic study of nonlinear differential equations within Sobolev spaces, focusing on mild solutions and their qualitative properties. An iterative reconstruction method is developed to obtain uniform a priori bounds, which ensure… read more here.

Keywords: priori uniform; theoretic tools; measure theoretic; tools long ... See more keywords