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A view on multiple recurrence |
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| Affiliation: | 1. Department of Mathematics, Howard University, Washington, DC 20059, USA;2. Department of Pure Mathematics, University of Leeds, Leeds LS2 9J2, UK;3. Université de Lyon, Université Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F69622 Villeurbanne Cedex, France |
| Abstract: | In this note we present a proof of multiple recurrence for ergodic systems (and thereby of Szemerédi’s theorem) being a mixture of three known proofs. It is based on a conditional version of the Jacobs–de Leeuw–Glicksberg decomposition and properties of the Gowers–Host–Kra uniformity seminorms. |
| Keywords: | Multiple recurrence Distal factors of finite order Gowers–Host–Kra seminorms Conditional Jacobs–de Leeuw–Glicksberg decomposition |
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