Minimal stretch factors of orientation-reversing fully-punctured pseudo-Anosov maps

Abstract

We show that the stretch factor $\lambda (f)$ of an orientation-reversing fully-punctured pseudo-Anosov map $f$ on a finite-type orientable surface $S$, with $-\chi (S)\ge 4$ and having at least two puncture orbits, satisfies the inequality $\lambda (f{)}^{-\chi (S)}\ge {\sigma }^2$, where $\sigma =1+\sqrt{2}$ is the silver ratio. We provide examples showing that this bound is asymptotically sharp. This extends previous results of Hironaka and the third author to orientation-reversing maps.

v2 - 27 pages, 6 figures; to appear in Transactions of the American Mathematical Society

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• On the minimal spectral radii of skew-reciprocal integer matrices