Bifurcation values and monodromy of mixed polynomials

TL;DR

This paper investigates the bifurcation values of real polynomial maps from ^{2n} to ^2, highlighting differences from complex cases and emphasizing real-specific phenomena at infinity.

Contribution

It formulates real analogues of known complex polynomial structure results, focusing on bifurcation values and asymptotic regularity in real polynomial maps.

Findings

Characterization of bifurcation values for real polynomial maps

Identification of real-specific phenomena at infinity

Extension of complex polynomial results to real case

Abstract

We study the bifurcation values of real polynomial maps $f: \bR^{2n} \to \bR^2$ which reflect the lack of asymptotic regularity at infinity. We formulate real counterparts of some structure results which have been previously proved in case of complex polynomials by Kushnirenko, N\'emethi and Zaharia and other authors, emphasizing the typical real phenomena that occur.