On topological entropy of group actions on 𝑆¹

Watanabe, Nobuya

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

On topological entropy of group actions on $S^ 1$
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Proc. Amer. Math. Soc. 106 (1989), 245-249 Request permission

Abstract:

In this paper, we show that a surface group action on ${S^1}$ with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on ${S^1}$ 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.

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