### Abstract

We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. For each point in the coordinate plane, we first compute the corresponding monodromy representation by numerical integration along certain loops. Then we decide whether the representation is discrete by applying Jørgensen's theory on the quasi-Fuchsian space of once-punctured tori.

Original language | English |
---|---|

Pages (from-to) | 51-60 |

Number of pages | 10 |

Journal | Experimental Mathematics |

Volume | 15 |

Issue number | 1 |

Publication status | Published - 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bers embedding
- Kleinian groups
- Teichmüller space

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Experimental Mathematics*,

*15*(1), 51-60.

**Drawing bers embeddings of the teichmüller space of once-punctured tori.** / Komori, Yohei; Sugawa, Toshiyuki; Wada, Masaaki; Yamashita, Yasushi.

Research output: Contribution to journal › Article

*Experimental Mathematics*, vol. 15, no. 1, pp. 51-60.

}

TY - JOUR

T1 - Drawing bers embeddings of the teichmüller space of once-punctured tori

AU - Komori, Yohei

AU - Sugawa, Toshiyuki

AU - Wada, Masaaki

AU - Yamashita, Yasushi

PY - 2006

Y1 - 2006

N2 - We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. For each point in the coordinate plane, we first compute the corresponding monodromy representation by numerical integration along certain loops. Then we decide whether the representation is discrete by applying Jørgensen's theory on the quasi-Fuchsian space of once-punctured tori.

AB - We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. For each point in the coordinate plane, we first compute the corresponding monodromy representation by numerical integration along certain loops. Then we decide whether the representation is discrete by applying Jørgensen's theory on the quasi-Fuchsian space of once-punctured tori.

KW - Bers embedding

KW - Kleinian groups

KW - Teichmüller space

UR - http://www.scopus.com/inward/record.url?scp=33745652976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745652976&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33745652976

VL - 15

SP - 51

EP - 60

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

IS - 1

ER -