Pseudo-Anosov map

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In mathematics, specifically in topology, a pseudo-Anosov map is a type of homeomorphism of a surface to itself. William Thurston coined the term when he provided his classification of homeomorphisms of a surface.

A homeomorphism

f : M → M

of a compact oriented surface M is called pseudo-Anosov if it preserves a transverse pair of foliations with measure, with finitely many singularities, and there is a number k > 1 such that one measure is expanded by k and the other is contracted by 1/k.

[edit] References

Good references are

W. Thurston, "On the geometry and dynamics of diffeomorphisms of surfaces," Bull. Amer. Math. Soc. vol 19 (1988), 417-431
A. Fathi, F. Laudenbach, and V. Poénaru, "Travaux de Thurston sur les surfaces," Asterisque, Vols. 66 and 67 (1979).