In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.
@article{urn:eudml:doc:41577, title = {Enveloppe galoisienne d'une application rationnelle de P1.}, journal = {Publicacions Matem\`atiques}, volume = {50}, year = {2006}, pages = {191-202}, zbl = {1137.37022}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41577} }
Casale, Guy. Enveloppe galoisienne d'une application rationnelle de P1.. Publicacions Matemàtiques, Tome 50 (2006) pp. 191-202. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41577/