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The nonexistence of sensitive commutative group actions on graphs

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Abstract

In this paper, we observe a special kind of continuous functions on graphs. By estimating the integrals of these functions, we prove that there are no sensitive commutative group actions on graphs. Furthermore, we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it, which answers negatively a question proposed by Kato in 1993.

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Authors and Affiliations

  1. Institute of Mathematics, Shantou University, Shantou, 515063, China

    Jie-hua Mai

  2. School of Mathematical Sciences, Suzhou University, Suzhou, 215006, China

    En-hui Shi

Authors
  1. Jie-hua Mai
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  2. En-hui Shi
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Corresponding author

Correspondence to En-hui Shi.

Additional information

The work was supported by the Special Foundation of National Prior Basic Researches of China (Grant No. G1999075108) and partially supported by the National Natural Science Foundation of China (Grant No. 10501042)

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Mai, Jh., Shi, Eh. The nonexistence of sensitive commutative group actions on graphs. SCI CHINA SER A 50, 1197–1204 (2007). https://doi.org/10.1007/s11425-007-0059-7

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  • DOI: https://doi.org/10.1007/s11425-007-0059-7

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