Méthodes de changement d’échelles en analyse complexe

François Berteloot[1]

  • [1] Université P. Sabatier, Toulouse III, Lab. Émile Picard, Bât. 1R2, 31062 Toulouse Cedex 9, France.

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

  • Volume: 15, Issue: 3, page 427-483
  • ISSN: 0240-2963

Abstract

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We discuss several rescaling methods in complex analysis and geometry and apply them to get elementary proofs of some classical results. The Bloch principle plays an important role in our approach and yields to a somewhat unified point of view.

How to cite

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Berteloot, François. "Méthodes de changement d’échelles en analyse complexe." Annales de la faculté des sciences de Toulouse Mathématiques 15.3 (2006): 427-483. <http://eudml.org/doc/10004>.

@article{Berteloot2006,
abstract = {Nous mettons en perspective différentes méthodes de changement d’échelles et illustrons leur pertinence en mettant sur pieds des preuves simples et élémentaires de plusieurs théorèmes biens connus en analyse ou géométrie complexe. Les situations abordées sont variées et la plupart des théorèmes démontrés sont des classiques initialement obtenus entre la fin du xixe  et la seconde moitié du xxe  siècle.},
affiliation = {Université P. Sabatier, Toulouse III, Lab. Émile Picard, Bât. 1R2, 31062 Toulouse Cedex 9, France.},
author = {Berteloot, François},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {rescaling methods; Bloch principle; renormalizations of holomorphic disks; integer curves; Zalcman renormalization process; dilatation of coordinates; Pinchuk method of coordinate dilatation; Julia ensembles of rational fractions; hyperbolicity in the Kobayashi sense; biholomorphisms; Kobayashi metric compartment; Wong-Rosay theorem; Fefferman theorem on the differentiable extension of biholomorphisms; dilatation of holomorphic germs; normalization and linearization along orbits of holomorphic endomorphism; normalization of invertible germs},
language = {fre},
number = {3},
pages = {427-483},
publisher = {Université Paul Sabatier, Toulouse},
title = {Méthodes de changement d’échelles en analyse complexe},
url = {http://eudml.org/doc/10004},
volume = {15},
year = {2006},
}

TY - JOUR
AU - Berteloot, François
TI - Méthodes de changement d’échelles en analyse complexe
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2006
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 3
SP - 427
EP - 483
AB - Nous mettons en perspective différentes méthodes de changement d’échelles et illustrons leur pertinence en mettant sur pieds des preuves simples et élémentaires de plusieurs théorèmes biens connus en analyse ou géométrie complexe. Les situations abordées sont variées et la plupart des théorèmes démontrés sont des classiques initialement obtenus entre la fin du xixe  et la seconde moitié du xxe  siècle.
LA - fre
KW - rescaling methods; Bloch principle; renormalizations of holomorphic disks; integer curves; Zalcman renormalization process; dilatation of coordinates; Pinchuk method of coordinate dilatation; Julia ensembles of rational fractions; hyperbolicity in the Kobayashi sense; biholomorphisms; Kobayashi metric compartment; Wong-Rosay theorem; Fefferman theorem on the differentiable extension of biholomorphisms; dilatation of holomorphic germs; normalization and linearization along orbits of holomorphic endomorphism; normalization of invertible germs
UR - http://eudml.org/doc/10004
ER -

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