## Abstract

Assume *f *:*U * → C is a holomorphic map fixing 0 with derivative *λ*, where 0 *< *|*λ*| 1. If *λ *is not a root of unity, there is a formal power series *φ _{f} (z) *=

*z*+

*O(z*

^{2}

*)*such that

*φ*=

_{f}(λz)*f (φ*. This power series is unique and we denote by Rconv

_{f }(z))*( f ) ε*[0

*,*+∞] its radius of convergence. We denote by Rgeom

*( f )*the largest radius

*r ε*[0

*,*Rconv

*( f )*] such that

*φ*0

_{f }(D(*, r ))*is a subset of

*U*. In this paper, we present new elementary techniques for studying the maps

*f*→ Rconv

*( f )*and

*f*→ Rgeom

*( f )*. Contrary to previous approaches, our techniques do not involve studying the arithmetical properties of rotation numbers.

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

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 145 |

Issue number | 2 |

Pages (from-to) | 443-456 |

Number of pages | 14 |

ISSN | 0305-0041 |

DOIs | |

Publication status | Published - 6 May 2008 |

## Keywords

- Siegel disk
- conformal radius