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

Jacek Chądzyński; Tadeusz Krasiński

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 3, page 291-302
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jacek Chądzyński, and 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 57.3 (1992): 291-302. <http://eudml.org/doc/275853>.

@article{JacekChądzyński1992,
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.},
author = {Jacek Chądzyński, Tadeusz Krasiński},
journal = {Annales Polonici Mathematici},
keywords = {Łojasiewicz exponent at infinity; polynomial mappings; polynomial automorphism; polynomial mapping},
language = {eng},
number = {3},
pages = {291-302},
title = {On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²},
url = {http://eudml.org/doc/275853},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Jacek Chądzyński
AU - Tadeusz Krasiński
TI - On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 3
SP - 291
EP - 302
AB - 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.
LA - eng
KW - Łojasiewicz exponent at infinity; polynomial mappings; polynomial automorphism; polynomial mapping
UR - http://eudml.org/doc/275853
ER -

References

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  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. Zbl0685.32006
  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. Zbl0578.32013
  6. [P₂] A. Płoski, On the growth of proper polynomial mappings, Ann. Polon. Math. 45 (1985), 297-309. Zbl0584.32006

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