Combinatorial independence and sofic entropy

DOI10.1007/s40304-013-0001-yzbMath1315.37025arXiv1208.2464OpenAlexW2962766089MaRDI QIDQ376064

Hanfeng Li, David Kerr

Publication date: 1 November 2013

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.2464

zbMATH Keywords

independencetopological entropyLi-Yorke chaossofic entropyalgebraic actionentropy tuplesFuglede-Kadison determinantLoeb space

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Topological entropy (37B40)

Related Items (28)

Naive entropy of dynamical systems ⋮ Fuglede-Kadison determinants and sofic entropy ⋮ Positive entropy implies chaos along any infinite sequence ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Deterministic functions on amenable semigroups and a generalization of the Kamae-Weiss theorem on normality preservation ⋮ POLISH MODELS AND SOFIC ENTROPY ⋮ Mean Proximality, Mean Sensitivity and Mean Li–Yorke Chaos for Amenable Group Actions ⋮ On M-dynamics and Li-Yorke chaos of extensions of minimal dynamics ⋮ Stable sets and mean Li–Yorke chaos in positive entropy actions of bi-orderable amenable groups ⋮ Stable sets and mean Li-Yorke chaos in positive entropy systems ⋮ Weak equivalence to Bernoulli shifts for some algebraic actions ⋮ Recoding Lie algebraic subshifts ⋮ \({\Delta}\)-weakly mixing subset in positive entropy actions of a nilpotent group ⋮ Relative entropy and the Pinsker product formula for sofic groups ⋮ Mean Li-Yorke chaos along some good sequences ⋮ Asymptotic pairs, stable sets and chaos in positive entropy systems ⋮ Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics ⋮ Positive entropy actions of countable groups factor onto Bernoulli shifts ⋮ Examples in the entropy theory of countable group actions ⋮ Relative Entropy and Mean Li–Yorke Chaos for Biorderable Amenable Group Actions ⋮ Convex structures revisited ⋮ Garden of Eden and specification ⋮ Sofic mean length ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Combinatorial independence and naive entropy ⋮ Local entropy theory of a random dynamical system ⋮ Conditional entropy and fiber entropy for amenable group actions ⋮ Recent development of chaos theory in topological dynamics

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