Convergence of multiple ergodic averages for some commuting transformations

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dc.creatorFrantzikinakis, Nikos
dc.creatorKra, Bryna
dc.date2004-06-18
dc.date.accessioned2026-07-07T05:09:21Z
dc.date.available2026-07-07T05:09:21Z
dc.descriptionWe prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0406360
dc.identifierhttp://arxiv.org/abs/math/0406360
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71598
dc.subjectDynamical Systems
dc.subject37A30
dc.titleConvergence of multiple ergodic averages for some commuting transformations
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