Dynamics on sensitive and equicontinuous functions

Jie Li, Tao Yu, Tiaoying Zeng

DOI: http://dx.doi.org/10.12775/TMNA.2017.054


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.


Sensitivity; sensitive pairs; sensitive functions; equicontinuous functions; weak mixing

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