### Abstract

We show that if f : M → 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 T^{2} and a map h : M → T^{2} such that h is a semi-conjugacy and (M, h) is a branched covering space of 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.

Original language | English (US) |
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Pages (from-to) | 2183-2192 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 127 |

Issue number | 7 |

State | Published - Dec 1 1999 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Franks, J. M., & Rykken, E. (1999). Pseudo-anosov homeomorphisms with quadratic expansion.

*Proceedings of the American Mathematical Society*,*127*(7), 2183-2192.