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An uncountable ergodic Roth theorem and applications.
- Source :
- Discrete & Continuous Dynamical Systems: Series A; Nov2022, Vol. 42 Issue 11, p5509-5540, 32p
- Publication Year :
- 2022
-
Abstract
- We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous result of Bergelson, McCutcheon and Zhang, and complements a result of Zorin-Kranich. We establish the following two additional results: First, a combinatorial application about triangular patterns in certain subsets of the Cartesian square of arbitrary amenable groups, extending a result of Bergelson, McCutcheon and Zhang for countable amenable groups. Second, a new uniformity aspect in the double recurrence theorem for Γ -systems for uniformly amenable groups Γ. Our uncountable Roth theorem is crucial in the proof of both of these results. [ABSTRACT FROM AUTHOR]
- Subjects :
- ERGODIC theory
RAMSEY theory
UNIFORMITY
Subjects
Details
- Language :
- English
- ISSN :
- 10780947
- Volume :
- 42
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- Discrete & Continuous Dynamical Systems: Series A
- Publication Type :
- Academic Journal
- Accession number :
- 159630973
- Full Text :
- https://doi.org/10.3934/dcds.2022111