We charocterize the commuting polynomial automorphisms of C2, using their meromorphic extension to P2 and looking at their dynamics on the line at infinity.
@article{urn:eudml:doc:41498, title = {On commuting polynomial automorphisms of C2.}, journal = {Publicacions Matem\`atiques}, volume = {48}, year = {2004}, pages = {227-239}, zbl = {1119.14047}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41498} }
Bisi, Cinzia. On commuting polynomial automorphisms of C2.. Publicacions Matemàtiques, Tome 48 (2004) pp. 227-239. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41498/