On topological entropy of group actions on s

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)245-249
Number of pages5
JournalProceedings of the American Mathematical Society
Volume106
Issue number1
DOIs
Publication statusPublished - 1989

Fingerprint

Euler numbers
Topological Entropy
Group Action
Entropy
Exponential Growth
Absolute value
Wood

Keywords

  • Euler number
  • Surface group action
  • Topological entropy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On topological entropy of group actions on s. / Watanabe, Nobuya.

In: Proceedings of the American Mathematical Society, Vol. 106, No. 1, 1989, p. 245-249.

Research output: Contribution to journalArticle

@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",
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

Y1 - 1989

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

VL - 106

SP - 245

EP - 249

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -