Infinitely many lattice surfaces with special pseudo-Anosov maps

2012/10/04 by Kariane Calta, Thomas A. Schmidt, Calta, Kariane +1
Mathematics · #37D99 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37D99

paper · pdf · doi:10.48550/arxiv.1210.1293

13 pages, 2 figures

arxiv created 2012/10/04 · arxiv updated 2012/10/05

Abstract

We give explicit pseudo-Anosov homeomorphisms with vanishing Sah-Arnoux-Fathi invariant. Any translation surface whose Veech group is commensurable to any of a large class of triangle groups is shown to have an affine pseudo-Anosov homeomorphism of this type. We also apply a reduction to finite triangle groups and thereby show the existence of non-parabolic elements in the periodic field of certain translation surfaces.

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