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Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex

Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex

Let M be a hyperbolic fibered 3-manifold whose first Betti number is greater than 1 and let S be a fiber with pseudo-Anosov monodromy \psi . We show that there exists a sequence (R_n, \psi_n) of fibers and monodromies contained in the fibered cone of (S,\psi) such that the asymptotic …