Constructing pseudo-Anosovs from expanding interval maps

2021/01/05 by Farber, Ethan
#37E30 (Primary) 37E05 #57K20 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2101.01721

Abstract

We investigate a phenomenon observed by W. Thurston wherein one constructs a pseudo-Anosov homeomorphism on the limit set of a certain lift of a piecewise-linear expanding interval map. We reconcile this construction with a special subclass of generalized pseudo-Anosovs, first defined by de Carvalho. From there we classify the circumstances under which this construction produces a pseudo-Anosov. As an application, we produce for each g ≥ 1 a pseudo-Anosov ϕ_g on the surface of genus g that preserves an algebraically primitive translation structure and whose dilatation λ_g is a Salem number.

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