On topological entropy of group actions on s

Nobuya Watanabe

doi:10.1090/S0002-9939-1989-0965946-X

On topological entropy of group actions on s

Nobuya Watanabe^*

^*Corresponding author for this work

School of Commerce

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we show that a surface group action on s¹ with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

Original language	English
Pages (from-to)	245-249
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	106
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1989-0965946-X
Publication status	Published - 1989 May

Keywords

Euler number
Surface group action
Topological entropy

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-1989-0965946-X

Cite this

@article{411d51f0f3d249e4a7d1834545f80942,

title = "On topological entropy of group actions on s",

abstract = "In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.",

keywords = "Euler number, Surface group action, Topological entropy",

author = "Nobuya Watanabe",

year = "1989",

month = may,

doi = "10.1090/S0002-9939-1989-0965946-X",

language = "English",

volume = "106",

pages = "245--249",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - On topological entropy of group actions on s

AU - Watanabe, Nobuya

PY - 1989/5

Y1 - 1989/5

N2 - In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

AB - In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

KW - Euler number

KW - Surface group action

KW - Topological entropy

UR - http://www.scopus.com/inward/record.url?scp=84966231342&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966231342&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1989-0965946-X

DO - 10.1090/S0002-9939-1989-0965946-X

M3 - Article

AN - SCOPUS:84966231342

SN - 0002-9939

VL - 106

SP - 245

EP - 249

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

On topological entropy of group actions on s

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this