We show that every local polynomial diffeomorphism (f,g) of the real plane such that deg f ≤ 3, deg g ≤ 3 is a global diffeomorphism.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-12, author = {Janusz Gwo\'zdziewicz}, title = {The Real Jacobian Conjecture for polynomials of degree 3}, journal = {Annales Polonici Mathematici}, volume = {77}, year = {2001}, pages = {121-125}, zbl = {0990.14023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-12} }
Janusz Gwoździewicz. The Real Jacobian Conjecture for polynomials of degree 3. Annales Polonici Mathematici, Tome 77 (2001) pp. 121-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-12/