Pseudo-Anosov maps and toral automorphisms

We give a construction of a pseudo-Anosov map of a surface starting from (and almost isomorphic to) a hyperbolic automorphism of an n-torus. The construction arises from a peano curve based on an invariant space-filling tree. This construction allows to confirm (for degree 3) a conjecture of Fried regarding stretch factors of pseudo-Anosov maps.

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