Some open problems on multiple ergodic averages

Details Some open problems on multiple ergodic averages Some open problems on multiple ergodic averages

2011-03-19

arxiv.org/abs/1103.3808v1

Mathematics

Dynamical Systems

Not to be published, but regular updates will be posted here: http://www.math.uoc.gr/~nikosf/OpenProblems.html

Scientific paper

This is a first attempt to organize a list of some open problems on three closely related topics: (i) The limiting behavior of single and multiple ergodic averages, (ii) Single and multiple recurrence properties of measure preserving systems, and (iii) Universal patterns, meaning, patterns that can be found in every set of integers with positive upper density, and related problems on higher dimensions. The list of problems is greatly influenced by my personal interests and is by no means meant to be a comprehensive list of open problems in the area widely known as ergodic Ramsey theory.

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