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Pseudo-Anosov homeomorphisms
with quadratic expansion


Authors: J. Franks and E. Rykken
Journal: Proc. Amer. Math. Soc. 127 (1999), 2183-2192
MSC (1991): Primary 58F15
DOI: https://doi.org/10.1090/S0002-9939-99-04731-0
Published electronically: February 17, 1999
MathSciNet review: 1485474
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 $f$.


References [Enhancements On Off] (What's this?)

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Additional Information

J. Franks
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Address at time of publication: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: john@math.nwu.edu

E. Rykken
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Address at time of publication: Department of Mathematics, Indiana University Northwest, Gary, Indiana 46408
Email: erykken@iunhaw1.iun.indiana.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04731-0
Received by editor(s): August 22, 1997
Received by editor(s) in revised form: October 1, 1997
Published electronically: February 17, 1999
Communicated by: Mary Rees
Article copyright: © Copyright 1999 American Mathematical Society