Infinite-step nilsystems, independence and complexity

DOI10.1017/S0143385711000861zbMath1268.37019arXiv1105.3584MaRDI QIDQ4911065

Pandeng Dong, Song Shao, Sebastián Donoso, Alejandro Maass, Xiang Dong Ye

Publication date: 13 March 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.3584

zbMATH Keywords

topological complexity\(\infty\)-step nilsystemsIP-independence setsminimal distal systemsminimal nilsystemsnon-trivial pairs

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Topological entropy (37B40)

Related Items (22)

Independence and almost automorphy of higher order ⋮ Topological complexity, minimality and systems of order two on torus ⋮ Some open problems on multiple ergodic averages ⋮ Topological characteristic factors and independence along arithmetic progressions ⋮ Affine transformation with zero entropy and nilsystems ⋮ Dynamical parallelepipeds in minimal systems ⋮ Polynomial orbits in totally minimal systems ⋮ Top-nilpotent enveloping semigroups and pro-nilsystems ⋮ Characterizations of distality via weak equicontinuity ⋮ Regionally proximal relation of order \(d\) along arithmetic progressions and nilsystems ⋮ Polynomial mean complexity and logarithmic Sarnak conjecture ⋮ Sensitivity, proximal extension and higher order almost automorphy ⋮ Variations on topological recurrence ⋮ Nil Bohr-sets and almost automorphy of higher order ⋮ Regionally proximal relation of order \(d\) is an equivalence one for minimal systems and a combinatorial consequence ⋮ Null systems in the non-minimal case ⋮ Maximal factors of order \(d\) of dynamical cubespaces ⋮ The logarithmic Sarnak conjecture for ergodic weights ⋮ \(\mathrm{IP}_r^\ast\)-recurrence and nilsystems ⋮ Measurable sensitivity via Furstenberg families ⋮ Complexity of nilsystems and systems lacking nilfactors ⋮ Pointwise convergence of multiple ergodic averages and strictly ergodic models

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