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.
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.
@article{AFST_2006_6_15_3_427_0, author = {Berteloot, Fran\c{c}ois}, title = {M\'ethodes de changement d{\textquoteright}\'echelles en analyse complexe}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {427--483}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {6e s{\'e}rie, 15}, number = {3}, year = {2006}, doi = {10.5802/afst.1127}, zbl = {1123.37019}, mrnumber = {2246412}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/afst.1127/} }
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 SP - 427 EP - 483 VL - 15 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1127/ DO - 10.5802/afst.1127 LA - fr ID - AFST_2006_6_15_3_427_0 ER -
%0 Journal Article %A Berteloot, François %T Méthodes de changement d’échelles en analyse complexe %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2006 %P 427-483 %V 15 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1127/ %R 10.5802/afst.1127 %G fr %F AFST_2006_6_15_3_427_0
Berteloot, François. Méthodes de changement d’échelles en analyse complexe. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 3, pp. 427-483. doi : 10.5802/afst.1127. http://www.numdam.org/articles/10.5802/afst.1127/
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