The discrete Markus–Yamabe problem for symmetric planar polynomial maps

We probe deeper into the discrete Markus–Yamabe question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the discrete Markus–Yamabe question are those possessing Z2Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map.