A Note on the Entropy for Heisenberg Group Actions on the Torus  

作　　者：Yu ZHANG Yu Jun ZHU 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第10期2324-2336,共13页数学学报（英文版）

基　　金：Supported by NSFC (Grant Nos. 12171400, 12126102)。

摘　　要：In this paper,the entropy of discrete Heisenberg group actions is considered.Let α be a discrete Heisenberg group action on a compact metric space X.Two types of entropies,h and h(α)are introduced,in which h is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then h is zero and h(α) can be expressed via the eigenvalues of the matrices.

关 键 词：ENTROPY Heisenberg group action natural extension TORUS 

分 类 号：O189.11[理学—数学]