Asymptotic pairs, stable sets and chaos in positive entropy systems
  We consider positive entropy $G$-systems for certain countable, discrete, infinite left-orderable amenable groups $G$. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the stable sets. Examples are given for the case of integer lattice groups, the Heisenberg group, and the groups of integral unipotent upper triangular matrices. 
Wen Huang, Leiye Xu and Yingfei Yi
math.DS math.FA