Sur la Linéarisation de Certains Sous Groupes de Difféomorphismes Polynomiaux du Plan et les Enveloppes D'holomorphie

D. Cerveau; J. J. Loeb

doi:10.1007/BF02922040

Sur la Linéarisation de Certains Sous Groupes de Difféomorphismes Polynomiaux du Plan et les Enveloppes D'holomorphie

Translated title of the contribution: On the linearization of some polynomial diffeomorphism subgroups of the plan and the envelope of holomorphy

D. Cerveau^*
, J. J. Loeb

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

Aut ₀(ℂ ²) let be the polynomial automorphism group of ℂ ² that leaves the origin fixed. Which are the subgroups G that are algebraically linearisable? We assume here that G is formally linearisable at the origin to a linear subgroup J ¹G. We give several cases of linearisation, among others, the case where j ¹G contains a contracting and an hyperbolic elements and the case where J ¹ G = SL(2, ℤ). Elements of complex dynamics in dimension two and the theory of envelope of holomorphy are used in the proofs.

Translated title of the contribution	On the linearization of some polynomial diffeomorphism subgroups of the plan and the envelope of holomorphy
Original language	French
Pages (from-to)	203-221
Number of pages	19
Journal	Journal of Geometric Analysis
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/BF02922040
State	Published - 2002

Keywords

hyperbolictity
linearization
polynomial authomorphisms

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF02922040

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title = "Sur la Lin{\'e}arisation de Certains Sous Groupes de Diff{\'e}omorphismes Polynomiaux du Plan et les Enveloppes D'holomorphie",

abstract = "Aut 0(ℂ 2) let be the polynomial automorphism group of ℂ 2 that leaves the origin fixed. Which are the subgroups G that are algebraically linearisable? We assume here that G is formally linearisable at the origin to a linear subgroup J 1G. We give several cases of linearisation, among others, the case where j 1G contains a contracting and an hyperbolic elements and the case where J 1 G = SL(2, ℤ). Elements of complex dynamics in dimension two and the theory of envelope of holomorphy are used in the proofs.",

keywords = "hyperbolictity, linearization, polynomial authomorphisms",

author = "D. Cerveau and Loeb, \{J. J.\}",

year = "2002",

doi = "10.1007/BF02922040",

language = "French",

volume = "12",

pages = "203--221",

journal = "Journal of Geometric Analysis",

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T1 - Sur la Linéarisation de Certains Sous Groupes de Difféomorphismes Polynomiaux du Plan et les Enveloppes D'holomorphie

AU - Cerveau, D.

AU - Loeb, J. J.

PY - 2002

Y1 - 2002

N2 - Aut 0(ℂ 2) let be the polynomial automorphism group of ℂ 2 that leaves the origin fixed. Which are the subgroups G that are algebraically linearisable? We assume here that G is formally linearisable at the origin to a linear subgroup J 1G. We give several cases of linearisation, among others, the case where j 1G contains a contracting and an hyperbolic elements and the case where J 1 G = SL(2, ℤ). Elements of complex dynamics in dimension two and the theory of envelope of holomorphy are used in the proofs.

AB - Aut 0(ℂ 2) let be the polynomial automorphism group of ℂ 2 that leaves the origin fixed. Which are the subgroups G that are algebraically linearisable? We assume here that G is formally linearisable at the origin to a linear subgroup J 1G. We give several cases of linearisation, among others, the case where j 1G contains a contracting and an hyperbolic elements and the case where J 1 G = SL(2, ℤ). Elements of complex dynamics in dimension two and the theory of envelope of holomorphy are used in the proofs.

KW - hyperbolictity

KW - linearization

KW - polynomial authomorphisms

UR - https://www.scopus.com/pages/publications/0141637239

U2 - 10.1007/BF02922040

DO - 10.1007/BF02922040

M3 - Article

AN - SCOPUS:0141637239

SN - 1050-6926

VL - 12

SP - 203

EP - 221

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

Sur la Linéarisation de Certains Sous Groupes de Difféomorphismes Polynomiaux du Plan et les Enveloppes D'holomorphie

Abstract

Keywords

ASJC Scopus subject areas

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