On Weak Rigidity and Weakly Mixing Enveloping Semigroups

Author

Ethan Akin, Missouri University of Science and TechnologyFollow
Eli Glasne
Benjamin Weiss

Abstract

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.

Recommended Citation

E. Akin et al., "On Weak Rigidity and Weakly Mixing Enveloping Semigroups," Contemporary Mathematics, vol. 744, pp. 181 - 190, American Mathematical Society, Jan 2020.

The definitive version is available at https://doi.org/10.1090/conm/744/14985

Department(s)

Mathematics and Statistics

Keywords and Phrases

Enveloping semigroup; Horocyclic flow; Weak mixing; Weak rigidity

International Standard Serial Number (ISSN)

1098-3627; 0271-4132

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 2020