Abstract
Let \eta be an arbitrary countable ordinal. Using results of Bourgain, Gamburd, and Sarnak on compact systems with spectral gap, we show the existence of an action of the free group on three generators F_3 on a compact metric space X , admitting an invariant probability measure \mu , such that the resulting dynamical system (X,\mu,F_3) is strongly ergodic and distal of rank \eta . In particular, this shows that there is an F_3 system which is strongly ergodic but not compact. This result answers the open question whether such actions exist.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
