Towards effective detection of the bifurcation locus of real polynomial maps

TL;DR

This paper develops a method to detect the bifurcation locus of real polynomial maps with multiple outputs using rational arcs, addressing a problem posed by Jelonek and Kurdyka.

Contribution

It provides an effective estimation technique for identifying the nontrivial bifurcation locus of polynomial maps from R^n to R^p for p>1.

Findings

Introduces a rational arc-based detection method.

Offers an effective estimation of the bifurcation locus.

Addresses a previously open problem in the field.

Abstract

We answer to a problem raised by recent work of Jelonek and Kurdyka: how can one detect by rational arcs the bifurcation locus of a polynomial map $\bR^n\to\bR^p$ in case $p>1$. We describe an effective estimation of the "nontrivial" part of the bifurcation locus.