Orientation-preserving self-homeomorphisms of the surface of genus two have points of period at most two

Dicks, Warren; Llibre, Jaume

doi:10.1090/S0002-9939-96-03131-0

Orientation-preserving self-homeomorphisms of the surface of genus two have points of period at most two
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by Warren Dicks and Jaume Llibre PDF

Proc. Amer. Math. Soc. 124 (1996), 1583-1591 Request permission

Abstract:

We show that for any orientation-preserving self-homeomorphism $\alpha$ of the double torus $\Sigma _{2}$ there exists a point $p$ of $\Sigma _{2}$ such that $\alpha (\alpha (p)) = p$. This answers a question raised by Jakob Nielsen in 1942.

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