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- W4300794987 abstract "We prove a variant of the multidimensional polynomial Szemer'edi theorem of Bergelson and Leibman where one replaces polynomial sequences with other sparse sequences defined by functions that belong to some Hardy field and satisfy certain growth conditions. We do this by studying the limiting behavior of the corresponding multiple ergodic averages and obtaining a simple limit formula. A consequence of this formula in topological dynamics shows denseness of certain orbits when the iterates are restricted to suitably chosen sparse subsequences. Another consequence is that every syndetic set of integers contains certain non-shift invariant patterns, and every finite coloring of $N$, with each color class a syndetic set, contains certain polychromatic patterns, results very particular to our non-polynomial setup." @default.
- W4300794987 created "2022-10-04" @default.
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- W4300794987 date "2012-02-21" @default.
- W4300794987 modified "2023-09-26" @default.
- W4300794987 title "A multidimensional Szemeredi theorem for Hardy sequences of different growth" @default.
- W4300794987 doi "https://doi.org/10.48550/arxiv.1202.4784" @default.
- W4300794987 hasPublicationYear "2012" @default.
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