Conjugacies between rational maps and extremal quasiconformal maps

Conjugacies between Rational Maps and Extremal Quasiconformal Maps

We show that two rational maps which are K-quasiconformally combinatorially equivalent are K-quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy. The Teichmüller theory is a powerful tool in the study of complex analytic dynamics. In addition to the work of D. Sullivan [Su] and W. Thurston (r...

Computing Extremal Quasiconformal Maps

Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. A natural extension to the space of conformal maps is the richer space of quasiconformal maps of bounded conformal distortion. Extremal quasiconformal maps, that is, maps min...

Quasi-symmetry of Conjugacies between Interval Maps

On Quasiconformal Harmonic Maps between Surfaces

It is proved the following theorem, if w is a quasiconformal harmonic mappings between two Riemann surfaces with smooth boundary and aproximate analytic metric, then w is a quasi-isometry with respect to Euclidean metric.

Explosion of smoothness for conjugacies between multimodal maps

Let f and g be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy h between f and g is C at a point in the nearby expanding set of f , then h is a smooth diffeomorphism in the basin of attraction of a renormalization interval of f . In particular, if f : I → I and g : J → J are Cr unimodal maps and h is C at a boundary of I then h is Cr in I.