The nonexistence of sensitive commutative group actions on graphs  

作　　者：Jie-hua MAI~1 En-hui SHI~(2+) 1 Institute of Mathematics,Shantou University,Shantou 515063,China 2 School of Mathematical Sciences,Suzhou University,Suzhou 215006,China 

出　　处：《Science China Mathematics》2007年第8期1197-1204,共8页中国科学：数学（英文版）

基　　金：the Special Foundation of National Prior Basic Researches of China(Grant No.G1999075108);partially supported by the National Natural Science Foundation of China(Grant No.10501042)

摘　　要：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.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.

关 键 词：HOMEOMORPHISM commutative group action graph map sensitivity EXPANSIVENESS infinite spiral curve 54H20 

分 类 号：O152.2[理学—数学]