| Abstrakt: |
Let f = (f1,...,fm) : ℝn → ℝm be a polynomial map; we consider the set Gf(r) = {x ∈ ℝn : |fi(x)| ≤ r, i = 1,...,m}. We show that if f satisfies the Mikhailov-Gindikin condition then: (i) Volume Gf(r) ≍ rθ( r)n-k-1, (ii) Cardinal , as r → ∞, where the exponents θ, k, θ′, k′ are determined explicitly in terms of the Newton polyhedra of f. Moreover, the polynomial maps satisfying the Mikhailov-Gindikin condition form an open subset of the set of polynomial maps having the same Newton polyhedron. [ABSTRACT FROM AUTHOR] |
