An Alternative Definition of Topological Entropy for Amenable Group Actions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-021-09547-0
Abstract: We extend the definition of topological entropy for any (not necessarily continuous) amenable groups acting on a compact space by defining entropy of arbitrary subsets of a product space. We investigate how this new notion… read more here.
Keywords: topological entropy; definition topological; entropy; entropy amenable ... See more keywords
Topological r-Entropy and Measure Theoretic r-Entropy for Amenable Group Actions
Sign Up to like & getrecommendations! 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
Mean Hausdorff dimension of some infinite dimensional fractals for amenable group actions
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0258258
Abstract: For the countable discrete amenable group actions, we calculate the mean Hausdorff dimensions of three types of infinite dimensional fractal systems, the self-similar systems, homogeneous systems in the infinite-dimensional torus, and the infinite dimensional-carpets. read more here.
Keywords: infinite dimensional; mean hausdorff; amenable group; hausdorff dimension ... See more keywords
On chaotic dynamics of the minimal centre of attraction of discrete amenable group actions
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DOI: 10.1080/14689367.2024.2410020
Abstract: Let X be a compact metric space, G be a countable discrete infinite amenable group continuously acting on X and $ \mathcal {F} $ F be a Følner sequence of G. In this paper, we… read more here.
Keywords: chaotic dynamics; discrete amenable; amenable group; centre attraction ... See more keywords
Entropies for factor maps of amenable group actions
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DOI: 10.1088/1361-6544/acc71c
Abstract: In this paper we study various entropies for factor maps of amenable group actions. We prove firstly theorem inequalities linking relative topological entropy and conditional topological entropy (for factor maps of amenable group actions) without… read more here.
Keywords: amenable group; maps amenable; group actions; entropy ... See more keywords