Mathematics – Dynamical Systems
Scientific paper
2011-03-19
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Not to be published, but regular updates will be posted here: http://www.math.uoc.gr/~nikosf/OpenProblems.html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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