### Abstract

Let f(z)=e^{2i\pi \theta} + z^2, where \theta is a quadratic
irrational. McMullen proved that the Siegel disk for f is
self-similar about the critical point, and we show that if \theta
= (\sqrt{5}-1)/2 is the golden mean, then there exists a triangle
contained in the Siegel disk, and with one vertex at the critical
point. This answers a 15 years old conjecture

Original language | English |
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Journal | Mathematical Research Letters |

Volume | 6 |

Issue number | 3-4 |

Pages (from-to) | 293-305 |

ISSN | 1073-2780 |

Publication status | Published - 1999 |

## Cite this

Buff, X., & Henriksen, C. (1999). Scaling Ratios and Triangles in Siegel Disks.

*Mathematical Research Letters*,*6*(3-4), 293-305.