Franks, J.; Rykken, E. Pseudo-Anosov homeomorphisms with quadratic expansion. (English) Zbl 0920.58035 Proc. Am. Math. Soc. 127, No. 7, 2183-2192 (1999). 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 \(f\). Cited in 1 ReviewCited in 4 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior Keywords:pseudo-Anosov homeomorphism; orientable surface; orientable unstable manifolds; quadratic expanding factor; hyperbolic toral automorphism; semi-conjugacy; affine structure PDFBibTeX XMLCite \textit{J. Franks} and \textit{E. Rykken}, Proc. Am. Math. Soc. 127, No. 7, 2183--2192 (1999; Zbl 0920.58035) Full Text: DOI