Abstract
A property P of a compact dynamical system (X, f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjective inverse limits. Many transitivity properties are residual. Weak disjointness from all property P systems is a residual property provided P is a residual property stronger than transitivity. Here two systems are weakly disjoint when their product is transitive. Our main result says that for an almost equicontinuous system (X, f) with associated monothetic group Λ, (X, f) is weakly disjoint from all P systems if the only P systems upon which Λ acts are trivial. We use this to prove that every monothetic group has an action which is weak mixing and topologically ergodic.
Recommended Citation
E. Akin and E. Glasner, "Residual Properties and Almost Equicontinuity," Journal D Analyse Mathematique, vol. 84, pp. 243 - 286, Springer, Jan 2001.
The definitive version is available at https://doi.org/10.1007/BF02788112
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
1565-8538; 0021-7670
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Springer, All rights reserved.
Publication Date
01 Jan 2001
