On weak rigidity and weakly mixing enveloping semigroups

Ethan Akin, Eli Glasne, Benjamin Weiss

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The question we deal with here, which was presented to us by Joe Auslander and Anima Nagar, is whether there is a nontrivial cascade (X, T) whose enveloping semigroup, as a dynamical system, is topologically weakly mixing (WM). After an introductory section recalling some definitions and classic results, we establish some necessary conditions for this to happen, and in the final section we show, using Ratners theory, that the enveloping semigroup of the time one map of a classical horocycle flow is weakly mixing.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages10
StatePublished - 2020

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


  • Enveloping semigroup
  • Horocyclic flow
  • Weak mixing
  • Weak rigidity


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