Attracting domains for semi-attractive transformations of Cp.

Monique Hakim

Publicacions Matemàtiques (1994)

  • Volume: 38, Issue: 2, page 479-499
  • ISSN: 0214-1493

Abstract

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Let F be a germ of analytic transformation of (Cp, 0). We say that F is semi-attractive at the origin, if F'(0) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C2 and F - Id has multiplicity k at the origin. This work has been inspired by two papers: one of P. Fatou (1924) and the other one of T. Ueda (1986).

How to cite

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Hakim, Monique. "Attracting domains for semi-attractive transformations of Cp.." Publicacions Matemàtiques 38.2 (1994): 479-499. <http://eudml.org/doc/41174>.

@article{Hakim1994,
abstract = {Let F be a germ of analytic transformation of (Cp, 0). We say that F is semi-attractive at the origin, if F'(0) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C2 and F - Id has multiplicity k at the origin. This work has been inspired by two papers: one of P. Fatou (1924) and the other one of T. Ueda (1986).},
author = {Hakim, Monique},
journal = {Publicacions Matemàtiques},
keywords = {Germen analítico; Sustitución isomórfica; Dominio de atracción; Transformación; semi-attractive transformations; domain of attraction},
language = {eng},
number = {2},
pages = {479-499},
title = {Attracting domains for semi-attractive transformations of Cp.},
url = {http://eudml.org/doc/41174},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Hakim, Monique
TI - Attracting domains for semi-attractive transformations of Cp.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 2
SP - 479
EP - 499
AB - Let F be a germ of analytic transformation of (Cp, 0). We say that F is semi-attractive at the origin, if F'(0) has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C2 and F - Id has multiplicity k at the origin. This work has been inspired by two papers: one of P. Fatou (1924) and the other one of T. Ueda (1986).
LA - eng
KW - Germen analítico; Sustitución isomórfica; Dominio de atracción; Transformación; semi-attractive transformations; domain of attraction
UR - http://eudml.org/doc/41174
ER -

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