Pseudo-anosov Homeomorphisms with Quadratic Expansion
نویسندگان
چکیده
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 T2 and a map h : M → T2 such that h is a semi-conjugacy and (M, h) is a branched covering space of T2. 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 .
منابع مشابه
Small dilatation pseudo-Anosov homeomorphisms and 3–manifolds
The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms φ : S → S, ranging over all surfaces S. More precisely, we consider pseudo-Anosov homeomorphisms φ : S → S with |χ(S)| log(λ(φ)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resul...
متن کاملInfinite sequence of fixed point free pseudo-Anosov homeomorphisms
We construct an infinite sequence of pseudo-Anosov homeomorphisms without fixed points and leaving invariant a sequence of orientable measured foliations on the same topological surface and the same stratum of the space of Abelian differentials. The existence of such a sequence shows that all pseudo-Anosov homeomorphisms fixing orientable measured foliations cannot be obtained by the Rauzy-Veec...
متن کاملExtensions, Quotients and Generalized Pseudo-anosov Maps
We describe a circle of ideas relating the dynamics of 2-dimensional homeomorphisms to that of 1-dimensional endomorphisms. This is used to introduce a new class of maps generalizing that of Thurston’s pseudo-Anosov homeomorphisms.
متن کاملOn the flux of pseudo-Anosov homeomorphisms
We exhibit a pseudo-Anosov homeomorphism of a surface S which acts trivially on H1(S; Z) and whose flux is nonzero.
متن کاملAn Implementation of the Bestvina-Handel Algorithm for Surface Homeomorphisms
In [BH95], Bestvina and Handel describe an effective algorithm that determines whether a given homeomorphism of an orientable, possibly punctured surface is pseudo-Anosov. We present a software package in ANSI-C that realizes this algorithm for surfaces with one puncture. Moreover, the package allows the user to define homeomorphisms in terms of Dehn twists, and in the pseudo-Anosov case it gen...
متن کامل