Affine transformation with zero entropy and nilsystems

作者：Lian Zhengxing^*

来源：Topology and Its Applications, 2017, 229: 126-140.

DOI：10.1016/j.topol.2017.06.01

• Affine transformation
• Nilsequence
• Zero entropy

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

• 出版日期2017-9-15