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

100%

Sękalski M.

Annales Polonici Mathematici

2005

tom 87

nr 1

229-235

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.

A polynomial with 2k critical values at infinity

63%

Gwoździewicz J., Sękalski M.

Annales Polonici Mathematici

2004

tom 84

nr 1

41-44

We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Sękalski M.

1 Gwoździewicz J.

1 2005

1 2004

Wyniki wyszukiwania

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

A polynomial with 2k critical values at infinity