On the size of linearization domains

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

lad f : → C have 0 som fikspunkt med eigenværdi λ, hvor 0 < |λ| 1. Hvis λ ikke er en enhedsrod, da findes der en entydigt bestemt formel potensrække φf (z) = z+O(z2) således at φf (λz) = f (φf (z)). Lad Rconv( f ) ε [0,+∞] betegne rækkens konvergensradius og lad Rgeom( f ) ε [0, Rconv( f )] betene den største radius r for hvilken φf (D(0, r ))  er en delmængde af U. In I denne artikel præsenterer vi nye elementære teknikker til at studre afbildningerne f → Rconv( f ) og f → Rgeom( f ). I modsætning til tidligere tilgange involverer vores tilgang ikke de artimetiske egenskaber af argumentet til λ.

OriginalsprogEngelsk
TidsskriftMathematical Proceedings of the Cambridge Philosophical Society
Vol/bind145
Udgave nummer2
Sider (fra-til)443-456
Antal sider14
ISSN0305-0041
DOI
StatusUdgivet - 6 maj 2008

Emneord

  • Siegel disk
  • konform radius

Citer dette

@article{411e58f0039211de9d17000ea68e967b,
title = "On the size of linearization domains",
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 φf (z) = z+O(z2) such that φf (λz) = f (φf (z)). This power series is unique and we denote by Rconv( f ) ε [0,+∞] its radius of convergence. We denote by Rgeom( f ) the largest radius r ε [0, Rconv( f )] such that φf (D(0, 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.",
keywords = "Siegel disk, konform radius, Siegel disk, conformal radius",
author = "Xavier Buff and Petersen, {Carsten Lunde}",
year = "2008",
month = "5",
day = "6",
doi = "10.1017/S0305004108001436",
language = "English",
volume = "145",
pages = "443--456",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "2",

}

On the size of linearization domains. / Buff, Xavier; Petersen, Carsten Lunde.

I: Mathematical Proceedings of the Cambridge Philosophical Society, Bind 145, Nr. 2, 06.05.2008, s. 443-456.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - On the size of linearization domains

AU - Buff, Xavier

AU - Petersen, Carsten Lunde

PY - 2008/5/6

Y1 - 2008/5/6

N2 - 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 φf (z) = z+O(z2) such that φf (λz) = f (φf (z)). This power series is unique and we denote by Rconv( f ) ε [0,+∞] its radius of convergence. We denote by Rgeom( f ) the largest radius r ε [0, Rconv( f )] such that φf (D(0, 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.

AB - 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 φf (z) = z+O(z2) such that φf (λz) = f (φf (z)). This power series is unique and we denote by Rconv( f ) ε [0,+∞] its radius of convergence. We denote by Rgeom( f ) the largest radius r ε [0, Rconv( f )] such that φf (D(0, 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.

KW - Siegel disk

KW - konform radius

KW - Siegel disk

KW - conformal radius

U2 - 10.1017/S0305004108001436

DO - 10.1017/S0305004108001436

M3 - Journal article

VL - 145

SP - 443

EP - 456

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -