A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.
@article{bwmeta1.element.bwnjournal-article-apmv57z3p291bwm, author = {Jacek Ch\k adzy\'nski and Tadeusz Krasi\'nski}, title = {On the \L ojasiewicz exponent at infinity for polynomial mappings of $\mathbb{C}$$^2$ into $\mathbb{C}$$^2$ and components of polynomial automorphisms of $\mathbb{C}$$^2$}, journal = {Annales Polonici Mathematici}, volume = {57}, year = {1992}, pages = {291-302}, zbl = {0791.14004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p291bwm} }
Jacek Chądzyński; Tadeusz Krasiński. On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ². Annales Polonici Mathematici, Tome 57 (1992) pp. 291-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p291bwm/
[000] [CK] J. Chądzyński and T. Krasiński, Exponent of growth of polynomial mappings of ℂ² into ℂ², in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa 1988, 147-160.
[001] [H] H. V. Ha, Nombres de Łojasiewicz et singularités à l'infini des polynômes de deux variables complexes, C. R. Acad. Sci. Paris Sér. I 311 (1990), 429-432.
[002] [HN] H. V. Ha et L. A. Nguyen, Le comportement géométrique à l’infini des polynômes de deux variables complexes, C. R. Acad. Sci. Paris Sér. I 309 (1989), 183-186. | Zbl 0685.32006
[003] [K] T. Krasiński, The level sets of polynomials in two variables and the jacobian conjecture, Acta Univ. Lodziensis, Wyd. UŁ, Łódź 1991 (in Polish).
[004] [P₁] A. Płoski, Une évaluation pour les sous-ensembles analytiques complexes, Bull. Polish Acad. Sci. Math. 31 (1983), 259-262. | Zbl 0578.32013
[005] [P₂] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309. | Zbl 0584.32006