The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps

Details The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps

2011-10-12

arxiv.org/abs/1110.2710v2

Mathematics

Dynamical Systems

Scientific paper

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 a?rmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an a?rmative 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.

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