TL;DR
This paper offers a new proof of multiple recurrence in ergodic systems, which underpins Szemerédi's theorem, by combining existing methods with novel insights involving the Jacobs-de Leeuw-Glicksberg decomposition and Gowers-Host-Kra seminorms.
Contribution
It introduces a proof that blends three known approaches to establish multiple recurrence, utilizing advanced decomposition and seminorm techniques.
Findings
Proof of multiple recurrence for ergodic systems
Connection to Szemerédi's theorem established
Utilizes a novel combination of existing methods
Abstract
In this note we present a proof of multiple recurrence for ergodic systems (and thereby of Szemer\'edi'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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Markov Chains and Monte Carlo Methods · Computability, Logic, AI Algorithms