Hyperbolic polynomials and multiparameter real analytic perturbation theory

Krzysztof Kurdyka, Laurentiu Paunescu

Let $P(x,z)=z^d+{\sum }_{i=1}^d{a}_i(x)z^{d-i}$ be a polynomial, where $a_i$ are real analytic functions in an open subset $U$ of ${\mathbb{R}}^n$. If for any $x\in U$ the polynomial $z\maps…