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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.

Multiplicity and the Łojasiewicz exponent

80%

Spodzieja S.

Annales Polonici Mathematici

2000

tom 73

nr 3

257-267

We give a formula for the multiplicity of a holomorphic mapping $f: ℂ^{n} ⊃ Ω → ℂ^{m}$, m > n, at an isolated zero, in terms of the degree of an analytic set at a point and the degree of a branched covering. We show that calculations of this multiplicity can be reduced to the case when m = n. We obtain an analogous result for the local Łojasiewicz exponent.

Ograniczanie wyników

3 Annales Polonici Mathematici

2 Chądzyński J.

2 Krasiński T.

1 Spodzieja S.

1 2000

1 1997

1 1995

Wyniki wyszukiwania

A set on which the local Łojasiewicz exponent is attained

Resultant and the Łojasiewicz exponent

Multiplicity and the Łojasiewicz exponent