Abstract
The notions of sensitive and equicontinuous functions under semigroup action are introduced and intensively studied. We show that a transitive system is sensitive if and only if it has a sensitive pair if and only if it has a sensitive function. While there exists a minimal non-weakly mixing system such that every non-constant continuous function is sensitive, and a topological dynamical system is weakly mixing if and only if it is sensitive consistently with respect to (at least) any two non-constant continuous functions. We also get a dichotomy result for minimal systems - every continuous function is either sensitive or equicontinuous.
Citation
Jie Li. Tao Yu. Tiaoying Zeng. "Dynamics on sensitive and equicontinuous functions." Topol. Methods Nonlinear Anal. 51 (2) 545 - 563, 2018. https://doi.org/10.12775/TMNA.2017.054