An example of local analytic q-difference equation : Analytic classification

Menous, Frédéric. "An example of local analytic q-difference equation : Analytic classification." Annales de la faculté des sciences de Toulouse Mathématiques 15.4 (2006): 773-814. <http://eudml.org/doc/10022>.

@article{Menous2006,
abstract = {Using the techniques developed by Jean Ecalle for the study of nonlinear differential equations, we prove that the $q$-difference equation\[ x \sigma \_q y = y + b ( y, x ) \]with $( \sigma _q f ) ( x ) = f ( q x )$ ($q &gt; 1$) and $b ( 0, 0 ) = \partial _y b ( 0, 0 ) = 0$ is analytically conjugated to one of the following equations :\[ x \sigma \_q y = y \quad \text\{ou\}\quad x \sigma \_q y = y + x \]},
affiliation = {UMR 8628, Département de Mathématiques, Université Paris-Sud, Centre d’Orsay, 91405 Orsay Cedex.},
author = {Menous, Frédéric},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {nonlinear analytic -difference equations},
language = {eng},
number = {4},
pages = {773-814},
publisher = {Université Paul Sabatier, Toulouse},
title = {An example of local analytic q-difference equation : Analytic classification},
url = {http://eudml.org/doc/10022},
volume = {15},
year = {2006},
}

TY - JOUR
AU - Menous, Frédéric
TI - An example of local analytic q-difference equation : Analytic classification
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2006
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 4
SP - 773
EP - 814
AB - Using the techniques developed by Jean Ecalle for the study of nonlinear differential equations, we prove that the $q$-difference equation\[ x \sigma _q y = y + b ( y, x ) \]with $( \sigma _q f ) ( x ) = f ( q x )$ ($q &gt; 1$) and $b ( 0, 0 ) = \partial _y b ( 0, 0 ) = 0$ is analytically conjugated to one of the following equations :\[ x \sigma _q y = y \quad \text{ou}\quad x \sigma _q y = y + x \]
LA - eng
KW - nonlinear analytic -difference equations
UR - http://eudml.org/doc/10022
ER -