arXiv:1511.06374 Abstract | arXiv Analytics

arXiv:1511.06374 [math.DS]Abstract References Reviews Resources

Affine transformation with zero entropy and nilsystems

Published 2015-11-19Version 1

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.

Comments: 13 pages. arXiv admin note: text overlap with arXiv:1407.1179 by other authors

Categories: math.DS

Subjects: 37B05

Keywords: zero entropy, nilsystems, orbit closure, study affine transformations, compact abelian groups

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