Invertible polynomial mappings via Newton non-degeneracy
نویسندگان
چکیده
We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.
منابع مشابه
Zeta Functions for Analytic Mappings, Log-principalization of Ideals, and Newton Polyhedra
In this paper we provide a geometric description of the possible poles of the Igusa local zeta function ZΦ(s, f) associated to an analytic mapping f = (f1, . . . , fl) : U(⊆ K ) → K, and a locally constant function Φ, with support in U , in terms of a log-principalizaton of the K [x]−ideal If = (f1, . . . , fl). Typically our new method provides a much shorter list of possible poles compared wi...
متن کاملLocal Zeta Functions of Degenerate Polynomials and Poles Associated with Degeneracy
We examine cases in which a polynomial f is degenerate with respect to its Newton polyhedron and when a pole results from degeneracy. We focus on polynomials which are reducible into linear factors, in particular those which are degenerate for all primes p with respect to the improper face of their Newton polyhedra. Two examples for which a new pole arises from degeneracy are computed and motiv...
متن کاملLocal Analytic Conjugacy of Resonant Analytic Mappings in Two Variables, in the Non-archimedean Setting
In this note, we consider locally invertible analytic mappings F in two dimensions with various linear parts. Our interest is in those maps possessing various types of resonance. We show for a variety of cases that resonant maps are analytically conjugated with polynomial normal forms, drawing comparisons and contrasts with the standard theory of local maps analytic in C. Moreover, we apply a g...
متن کاملMaximally positive polynomial systems supported on circuits
A real polynomial system with support W ⊂ Z is called maximally positive if all its complex solutions are positive solutions. A support W having n+ 2 elements is called a circuit. We previously showed that the number of non-degenerate positive solutions of a system supported on a circuitW ⊂ Z is at most m(W) + 1, where m(W) ≤ n is the degeneracy index of W . We prove that if a circuit W ⊂ Z sup...
متن کاملGeneric Asymptotics of Eigenvalues Using Min-plus Algebra
Abstract: We consider a square matrix Aǫ whose entries have first order asymptotics of the form (Aǫ)i j ∼ ai j ǫAi j when ǫ goes to 0, for some ai j ∈ C and Ai j ∈ R. We show that under a non-degeneracy condition, the order of magnitudes of the different eigenvalues ofAǫ are given by min-plus eigenvalues of min-plus Schur complements built from A = (Ai j ), or equivalently by generalized minima...
متن کامل