The Łojasiewicz exponent at infinity of a polynomial of two real variables

• Autorzy: Jankowski P.
• Języki publikacji: EN

Abstrakty

EN

It is shown that the Łojasiewicz exponent at infinity of a positively defined polynomial of two real variables is attained on the set of zeros of a partial derivative of this polynomial. The second result is that the set of the Łojasiewicz exponents at infinity of positively defined polynomials is equal to the set of rational numbers.

Słowa kluczowe

EN

Łojasiewicz exponent at infinity; polynomial mappings

PL

odwzorowanie wielomianu

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 1
• Strony: 25--31
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Jankowski P.

• Secondary School No 3, ul. Żeromskiego 26, 90-737 Łódź, Poland

Bibliografia

• [1] J. Chądzyński, T. Krasiński, Exponent of growth of polynomial mappings of C2 into C2, Banach Center Publ., PWN, 20 (1988) 146-160.
• [2] J. Chądzyński, T. Krasiński, On the Łojasiewicz exponent at infinity for polynomial mappings of C2 into C2 and components of polynomial automorphisms of C2, Ann. Polon. Math., (1992) 291-302.
• [3] J. Gwoździewicz, Growth at infinity of a polynomial with a compact zero set, in: Singularities Symposium - Łojasiewicz 70, Banach Center Publ., 44 (1998) 123-128.
• [4] E. A. Gorin, On asymptotic properties of polynomials and algebraic functions in several variables, Uspekhi Mat. Nauk, 16 (1961) 91-118.
• [5] J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61 (1968).