ArticleOriginal scientific text

Title

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

Authors 1, 1

Affiliations

  1. Institute of Mathematics, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland

Abstract

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.

Keywords

Łojasiewicz exponent at infinity, polynomial mappings, polynomial automorphism

Bibliography

  1. [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.
  2. [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.
  3. [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.
  4. [K] T. Krasiński, The level sets of polynomials in two variables and the jacobian conjecture, Acta Univ. Lodziensis, Wyd. UŁ, Łódź 1991 (in Polish).
  5. [P₁] A. Płoski, Une évaluation pour les sous-ensembles analytiques complexes, Bull. Polish Acad. Sci. Math. 31 (1983), 259-262.
  6. [P₂] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309.
Pages:
291-302
Main language of publication
English
Received
1992-06-11
Published
1992
Exact and natural sciences