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Approximate roots of pseudo-Anosov diffeomorphisms

T. M. Gendron (2009)

Annales de l’institut Fourier

The Root Conjecture predicts that every pseudo-Anosov diffeomorphism of a closed surface has Teichmüller approximate n th roots for all n 2 . In this paper, we replace the Teichmüller topology by the heights-widths topology – that is induced by convergence of tangent quadratic differentials with respect to both the heights and widths functionals – and show that every pseudo-Anosov diffeomorphism of a closed surface has heights-widths approximate n th roots for all n 2 .

Bounded geometry of quadrilaterals and variation of multipliers for rational maps

Kevin M. Pilgrim (2004)

Fundamenta Mathematicae

Let Q be the unit square in the plane and h: Q → h(Q) a quasiconformal map. When h is conformal off a certain self-similar set, the modulus of h(Q) is bounded independent of h. We apply this observation to give explicit estimates for the variation of multipliers of repelling fixed points under a "spinning" quasiconformal deformation of a particular cubic polynomial.

Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau (2008)

Annales scientifiques de l'École Normale Supérieure

In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...

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