The degree at infinity of the gradient of a polynomial in two real variables

• Autorzy: Maciej Sękalski
• Języki publikacji: EN

Abstrakty

EN

Let f:ℝ² → ℝ be a polynomial mapping with a finite number of critical points. We express the degree at infinity of the gradient ∇f in terms of the real branches at infinity of the level curves {f(x,y) = λ} for some λ ∈ ℝ. The formula obtained is a counterpart at infinity of the local formula due to Arnold.

Kategorie tematyczne

• 32B10: Germs of analytic sets, local parametrization
• 14P15: Real analytic and semianalytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 87
• Numer: 1
• Strony: 229-235

Daty

wydano

2005

Twórcy

autor

Maciej Sękalski

• Department of Mathematics, Technical University, Al. 1000LPP 7, 25-314 Kielce, Poland

Identyfikatory

DOI

10.4064/ap87-0-19