Nilfactors of \(\mathbb R^m\) and configurations in sets of positive upper density in \(\mathbb R^m\)

DOI10.1007/BF02789447zbMath1145.37005arXivmath/0505276MaRDI QIDQ2479616

Tamar Ziegler

Publication date: 1 April 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505276

zbMATH Keywords

geometric Ramsy theorynilfactors of \(\mathbb R^m\)-actionsset of positive upper density in \(\mathbb R^n\)

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) One-parameter continuous families of measure-preserving transformations (28D10)

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Cites Work

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• A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\)
• An ergodic Szemerédi theorem for commuting transformations
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Recent trends in Euclidean Ramsey theory
• Nonconventional ergodic averages and nilmanifolds
• Plane Sets with Positive Density at Infinity Contain all Large Distances
• Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
• Convergence of multiple ergodic averages for some commuting transformations
• Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
• Metric Classification of Ergodic Nilflows and Unipotent Affines

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