# Circle homeomorphisms and shears

@article{ari2009CircleHA, title={Circle homeomorphisms and shears}, author={Dragomir {\vS}ari{\'c}}, journal={arXiv: Geometric Topology}, year={2009} }

We give parameterizations of homeomorphisms, quasisymmetric maps and symmetric maps of the unit circle in terms of shear coordinates for the Farey tesselation.

## 10 Citations

### Shears for quasisymmetric maps

- MathematicsProceedings of the American Mathematical Society
- 2020

We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family…

### Shears for quasisymmetric maps

- Mathematics
- 2020

We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family…

### Circle homeomorphisms with square summable diamond shears

- Mathematics
- 2022

We introduce and study `2 spaces of homeomorphisms of the circle (up to Möbius transformations) with respect to two modular coordinates, namely shears and diamond shears along the edges of the Farey…

### Conformally natural extensions of continuous circle maps: II. The general case

- Mathematics
- 2017

We introduce a procedure for extending continuous circle maps in a conformally natural way to continuous maps from the closed disk, bounded by the circle to itself which generalizes Douady-Earle’s…

### Conformally natural extensions of continuous circle maps: II. The general case

- MathematicsJournal d'Analyse Mathématique
- 2017

We introduce a procedure for extending continuous circle maps in a conformally natural way to continuous maps from the closed disk, bounded by the circle to itself which generalizes Douady-Earle’s…

### Quasisymmetric maps, shears, lambda lengths and flips

- Mathematics
- 2022

. We study quasisymmetric maps, which act on the boundary of the hyperbolic plane, by looking at their action on the Farey triangulation. Our main results identify exactly which quasisymmetric maps…

### Characterization of the asymptotic Teichmüller space of the open unit disk through shears

- Mathematics
- 2013

We give a parametrization of the asymptotic Teichmuller space AT (D) of the open unit disk through a space of equivalent classes of the shear functions induced by quasisymmetric homeomorphisms on the…

### Ergodicity of the geodesic flow on symmetric surfaces

- Mathematics
- 2022

. We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface X that guarantee the surface X is of parabolic type. An interesting class of Riemann surfaces for this problem is the…

### Zygmund vector fields, Hilbert transform and Fourier coefficients in shear coordinates

- Mathematics
- 2011

We parametrize the space ${\cal Z}$ of Zygmund vector fields on the unit circle in terms of infinitesimal shear functions on the Farey tesselation. Then we express the Hilbert transform and the…

### Cross-ratio distortion and Douady–Earle extension: III. How to control the dilatation near the origin

- MathematicsAnnales Academiae Scientiarum Fennicae Mathematica
- 2019

In this paper, we study how the maximal dilatation of the Douady–Earle extension near the origin is controlled by the distortion of the boundary map on finitely many points. Consider the case of…

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