Multiple ergodic averages for variable polynomials

Andreas Koutsogiannis

doi:10.3934/dcds.2022067

Article Contents

2022, Volume 42, Issue 9: 4637-4668. Doi: 10.3934/dcds.2022067

This issue Previous Article Global well-posedness of the Cauchy problem for the Jordan–Moore–Gibson–Thompson equation with arbitrarily large higher-order Sobolev norms Next Article

Multiple ergodic averages for variable polynomials

Andreas Koutsogiannis

Aristotle University of Thessaloniki, Department of Mathematics, Thessaloniki, 54124, Greece

Dedicated to the loving memory of Aris Deligiannis, a great mentor

Received: October 31, 2021

Revised: February 28, 2022

Early access: May 2022

Published: August 2022

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Abstract

In this paper we study multiple ergodic averages for "good" variable polynomials. In particular, under an additional assumption, we show that these averages converge to the expected limit, making progress related to an open problem posted by Frantzikinakis ([13,Problem 10]). These general convergence results imply several variable extensions of classical recurrence, combinatorial and number theoretical results which are presented as well.

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Mathematics Subject Classification: Primary: 37A44; Secondary: 37A05, 11B25, 11B83, 05D10.

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