Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy
arXiv:1005.4148
Abstract
We prove that the dilatation of any pseudo-Anosov homeomorphism on a translation surface that belong to a hyperelliptic component is bounded from below uniformly by sqrt{2}. This is in contrast to Penner's asymptotic. Penner proved that the logarithm of the least dilatation of any pseudo-Anosov homeomorphism on a surface of genus g tends to zero at rate 1/g (as g goes to infinity). We also show that our uniform lower bound sqrt{2} is sharp. More precisely the least dilatation of a pseudo-Anosov on a genus g>1 translation surface in a hyperelliptic component belongs to the interval ]sqrt{2},sqrt{2}+2^{1-g}[. The proof uses the Rauzy-Veech induction.
33 pages, 4 figures
References in corpus (4)
- A family of pseudo-Anosov braids with small dilatation
- Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid
- Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior
- Classification of Rauzy classes in the moduli space of quadratic differentials