On the size of linearization domains

Xavier Buff; Carsten Lunde Petersen

doi:10.1017/S0305004108001436

On the size of linearization domains

Xavier Buff, Carsten Lunde Petersen

Matematik og Fysik (IMFUFA)

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstract

lad f :U → 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 φ_f(z) = z+O(z²) således at φ_f(λz) = f (φ_f (z)). Lad Rconv( f ) ε [0,+∞] betegne rækkens konvergensradius og lad Rgeom( f ) ε [0, Rconv( f )] betene den største radius r for hvilken φ_f(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.

Originalsprog	Engelsk
Tidsskrift	Mathematical Proceedings of the Cambridge Philosophical Society
Vol/bind	145
Udgave nummer	2
Sider (fra-til)	443-456
Antal sider	14
ISSN	0305-0041
DOI	https://doi.org/10.1017/S0305004108001436
Status	Udgivet - 6 maj 2008

Emneord

Siegel disk
konform radius

Link til dokument

10.1017/S0305004108001436

Citer dette

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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.",

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T1 - On the size of linearization domains

AU - Buff, Xavier

AU - Petersen, Carsten Lunde

PY - 2008/5/6

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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

SN - 0305-0041

VL - 145

SP - 443

EP - 456

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

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