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.


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
Full Text: DOI Euclid