Topological Semi-Conjugacies Between Adding Machines |
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| Authors: | Jie-Hua Mai Cui-Jun Liu Xin-He Liu |
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| Institution: | (1) Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, People’s Republic of China;(2) School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China;(3) Institute of Mathematics, Guangxi University, Nanning, Guangxi, 530004, People’s Republic of China |
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| Abstract: | Let K = (k
1, k
2, . . .) be a sequence of positive integers, and  be a topological group with a metric and an additive operation given. The adding machine f
K
is the addition-by-one map on Σ
K
. Buescu and Stewart (Ergodic Theory Dynam Syst 15:271–290, 1995), Block and Keesling (Topology Appl 140:151–161, 2004) and
Banks (Ergodic Theory Dynam Syst 17:505–529, 1997) obtained several equivalent conditions for which two adding machines are
topologically conjugate, respectively. In this paper, we have a further discussion about semi-conjugate relationship between
adding machines, and give some necessary and sufficient conditions for an adding machine to be semi-conjugate to another one.
Moveover, we also prove that a transitive translation on a compact subgroup of Σ
K
is isometrically conjugate to an adding machine.
Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday |
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| Keywords: | Adding machine Topological group Homomorphism Topological conjugacy Topological semi-conjugacy |
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