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In this paper, we try to describe the relationship between the differentiability of a quasisymmetric homeomorphism and the local Hausdorff dimension of the quasiline at a point. [ABSTRACT FROM AUTHOR]

This paper studies the quasisymmetric mappings on Moran sets. We introduce a generalized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure. [ABSTRACT FROM AUTHOR]

We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi's metric and Teichmüller's metric coincide with each other on the Teichmüller space of symmetric circle homeomorphisms. [ABSTRACT FROM AUTHOR]

Suppose f( z) is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim ( J( f) < 2. [ABSTRACT FROM AUTHOR]

In this work we study Lie symmetries of planar quasihomogeneous polynomial vector fields from different points of view, showing its integrability. Additionally, we show that certain perturbations of such vector fields which generalize the so-called degenerate infinity vector fields are also integrable. [ABSTRACT FROM AUTHOR]