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Exponent of growth of polynomial mappings of $C^{2}$ into $C^{2}$

Jacek Chadzyński; Tadeusz Krasiński — 1988

Banach Center Publications

The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero

Jacek Chadzyński; Tadeusz Krasiński — 1988

Banach Center Publications

A set on which the local Łojasiewicz exponent is attained

Jacek Chądzyński; Tadeusz Krasiński — 1997

Annales Polonici Mathematici

Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping $F = (f ₁, . . ., f ₘ) : U \to ℂ^{m}$ , F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.

A set on which the Łojasiewicz exponent at infinity is attained

Jacek Chądzyński; Tadeusz Krasiński — 1997

Annales Polonici Mathematici

We show that for a polynomial mapping $F = (f ₁, . . ., f ₘ) : ℂ^{n} \to ℂ^{m}$ the Łojasiewicz exponent $_{\infty} (F)$ of F is attained on the set $z \in ℂ^{n} : f ₁ (z) \cdot . . . \cdot f ₘ (z) = 0$ .

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

Jacek Chądzyński; Tadeusz Krasiński — 1992

Annales Polonici Mathematici

A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.

On the Łojasiewicz exponent for analytic curves

Jacek Chądzyński; Tadeusz Krasiński — 1998

Banach Center Publications

An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.

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Currently displaying 1 – 6 of 6

Exponent of growth of polynomial mappings of $C^{2}$ into $C^{2}$

The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero

A set on which the local Łojasiewicz exponent is attained

A set on which the Łojasiewicz exponent at infinity is attained

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

On the Łojasiewicz exponent for analytic curves

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Formula preview

Currently displaying 1 – 6 of 6

Exponent of growth of polynomial mappings of C 2 into C 2

The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero

A set on which the local Łojasiewicz exponent is attained

A set on which the Łojasiewicz exponent at infinity is attained

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

On the Łojasiewicz exponent for analytic curves

Exponent of growth of polynomial mappings of $C^{2}$ into $C^{2}$