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A set on which the Łojasiewicz exponent at infinity is attained

100%

Chądzyński J., Krasiński T.

Annales Polonici Mathematici

1997

tom 67

nr 2

191-197

We show that for a polynomial mapping $F = (f₁,..., fₘ): ℂ^n → ℂ^m$ the Łojasiewicz exponent $𝓛_∞(F)$ of F is attained on the set ${z ∈ ℂ^n: f₁(z) ·...· fₘ(z) = 0}$.

A set on which the local Łojasiewicz exponent is attained

100%

Chądzyński J., Krasiński T.

Annales Polonici Mathematici

1997

tom 67

nr 3

297-301

Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping $F = (f₁,..., fₘ): U → ℂ^m$, F(0) = 0, the Łojasiewicz exponent 𝓛₀(F) is attained on the set {z ∈ U: f₁(z)·...·fₘ(z) = 0}.

Resultant and the Łojasiewicz exponent

80%

Chądzyński J., Krasiński T.

Annales Polonici Mathematici

1995

tom 61

nr 1

95-100

An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.

On the Łojasiewicz exponent of the gradient of a polynomial function

80%

Lenarcik A.

Annales Polonici Mathematici

1999

tom 71

nr 3

211-239

Let $h = ∑ h_{αβ} X^αY^β$ be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that $|grad h(x,y)| ≥ c|(x,y)|^λ$ in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.

Ograniczanie wyników

4 Annales Polonici Mathematici

3 Chądzyński J.

3 Krasiński T.

1 Lenarcik A.

1 1999

2 1997

1 1995

Wyniki wyszukiwania

A set on which the Łojasiewicz exponent at infinity is attained

A set on which the local Łojasiewicz exponent is attained

Resultant and the Łojasiewicz exponent

On the Łojasiewicz exponent of the gradient of a polynomial function