Affine transformation with zero entropy and nilsystems

Abstract

In this paper, we study affine transformations on tori, nilmanifolds and compact abelian groups. For these systems, we show that an equivalent condition for zero entropy is the orbit closure of each point has a nice structure. To be precise, the affine systems on those spaces are zero entropy if and only if the orbit closure of each point is isomorphic to an inverse limit of nilsystems.

arXiv comment13 pages. arXiv admin note: text overlap with arXiv:1407.1179 by other authors