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 Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map. 
Bego\~na Alarc\'on, Sofia B. S. D. Castro and Isabel S. Labouriau
math.DS