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Here h is a pseudo-Anosov homeomorphism of a surface S while V is the set of isotopy classes of simple closed curves in S bounding essential disks in a fixed handlebody.\n  With the same hypothesis we show the distance of the splitting (S,V, h^n(V)) grows linearly with n, answering a question of A Casson. In addition we prove the converse of Hempel's theorem. 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