The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps
Dynamical Systems
2016-12-09 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1110.2710,
title = {The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps},
author = {Begoña Alarcón and Sofia B. S. D. Castro and Isabel S. Labouriau},
journal= {arXiv preprint arXiv:1110.2710},
year = {2016}
}