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The minimal dilatation of a genus-two surface. (English) Zbl 1153.37375

Summary: We show that the minimal dilatation of pseudo-Anosov homeomorphisms of a closed oriented genus-two surface is equal to the largest root of \(x^4-x^3-x^2-x+1\), which is approximately 1.72208.

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37B40 Topological entropy
57M60 Group actions on manifolds and cell complexes in low dimensions
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Full Text: DOI Euclid