Article ID Journal Published Year Pages File Type
4666235 Advances in Mathematics 2012 32 Pages PDF
Abstract

Inverse limits of nilsystems in topologically dynamical systems were characterized by Host, Kra and Maass recently. Namely, for each d∈Nd∈N a certain generalization of the regionally proximal relation was introduced, and for a distal minimal system it was shown that such a relation is an equivalence one, which determines the maximal dd-step nilfactor. One of the main results in this article is to show that the above results hold for a general minimal system.A combinatorial consequence is also deduced, which is the topological correspondence of the result obtained by Host and Kra for positive upper Banach density subsets using ergodic methods.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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