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Topological Methods in Nonlinear Analysis

Dynamics on sensitive and equicontinuous functions
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Dynamics on sensitive and equicontinuous functions

Authors

  • Jie Li
  • Tao Yu
  • Tiaoying Zeng

Keywords

Sensitivity, sensitive pairs, sensitive functions, equicontinuous functions, weak mixing

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.

References

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Published

2018-01-08

How to Cite

1.
LI, Jie, YU, Tao and ZENG, Tiaoying. Dynamics on sensitive and equicontinuous functions. Topological Methods in Nonlinear Analysis. Online. 8 January 2018. Vol. 51, no. 2, pp. 545 - 563. [Accessed 5 July 2025].
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Vol 51, No 2 (June 2018)

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