The boundary of a fibered face of the magic 3-manifold and the asymptotic behavior of the minimal pseudo-Anosovs dilatations

Abstract

Let ${\delta }_{g,n}$ be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus $g$ with $n$ punctures. Tsai proved that for any fixed $g\ge 2$, the logarithm of the minimal dilatation $\log {\delta }_{g,n}$ is on the order of $\frac{\log n}{n}$. The main result of this paper is that if $2g+1$ is relatively prime to $s$ or $s+1$ for each $0\le s\le g$, then $$\underset{n\to \infty }{\mathrm{limsup}}\frac{n\log {\delta }_{g,n}}{\log n}\le 2.$$

13 pages, 1 figures

References in corpus (3)

• A family of pseudo-Anosov braids with small dilatation
• Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior
• Sequences of pseudo-Anosov mapping classes and their asymptotic behavior