Abstract
In this note, we present a method of computing monodromies of projective structures on a once-punctured torus. This leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space. As a by-product, the value of the accessory parameter of a four-times punctured sphere will be calculated in a numerical way as well as the generators of a Fuchsian group uniformizing it. Finally, we observe the relation between the Schwarzian differential equation and Heun's differential equation in this special case.
| Original language | English |
|---|---|
| Journal | Conformal Geometry and Dynamics |
| Volume | 8 |
| Publication status | Published - 2004 Dec 1 |
| Externally published | Yes |
Keywords
- Accessory parameter
- Bending coordinates
- Bers embedding
- Monodromy
- Once-punctured torus
- Pleating ray
- Teichmueller space
- Teichmuller space
ASJC Scopus subject areas
- Geometry and Topology