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

2024/02/23 by Lanneau, Erwan, Liechti, Livio, Tsang, Chi Cheuk
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2402.15369

Abstract

We show that the stretch factor λ(f) of an orientation-reversing fully-punctured pseudo-Anosov map f on a finite-type orientable surface S, with -χ(S) ≥ 4 and having at least two puncture orbits, satisfies the inequality λ(f)^-χ(S) ≥ σ², where σ=1+√(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.

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