On the topological entropy of free semigroup actions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Wang, Yupan¹  Ma, Dongkui²  Lin, Xiaogang³ 

[1] S China Univ Technol, Sch Comp Sci & Engn, Guangzhou 510641, Guangdong, Peoples R China

[2] S China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[3] S China Univ Technol, Sch Business Adm, Guangzhou 510641, Guangdong, Peoples R China

关键词: Topological entropy;    Free semigroup actions;    Skew-product transformations;    Affine transformations;   

DOI  :  10.1016/j.jmaa.2015.11.038

来源: Elsevier

【 摘 要 】

We extend the notion the topological entropy of a free semigroup action defined by Bufetov [6] to the case of a free semigroup action on a metric space not necessarily compact, provide some properties of this extended topological entropy, extend the topological analogue of the classical Abramov-Rokhlin formula for the entropy of a skew product transformations with respect to a metric space not necessarily compact and give some bounds for the entropy for some particular systems such as a free semigroup with m generators of affine transformations on p-dimensional torus and smooth maps on a Riemannian manifold. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free