Exponent of growth of polynomial mappings of into
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
Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping , 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
We show that for a polynomial mapping the Łojasiewicz exponent of F is attained on the set .
On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²
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
An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.
Page 1