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 Z(2) as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.