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Pseudo-Anosov homeomorphisms with quadratic expansion. (English) Zbl 0920.58035

Summary: We show that if \( f: M \rightarrow M\) is a pseudo-Anosov homeomorphism on an orientable surface with oriented unstable manifolds and a quadratic expanding factor, then there is a hyperbolic toral automorphism on \(\mathbb{T}^2\) and a map \(h: M \rightarrow \mathbb{T}^2 \) such that \(h\) is a semi-conjugacy and \( (M, h) \) is a branched covering space of \( \mathbb{T}^2 \). We also give another characterization of pseudo-Anosov homeomorphisms with quadratic expansion in terms of the kinds of Euclidean foliations they admit which are compatible with the affine structure associated to \(f\).

MSC:

37D99 Dynamical systems with hyperbolic behavior
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