Picturing Pinchuk's Plane Polynomial Pair
摘要
Sergey Pinchuk discovered a class of pairs of real polynomials in two variables that have a nowhere vanishing Jacobian determinant and define maps of the real plane to itself that are not one-to-one. This paper describes the asymptotic behavior of one specific map in that class. The level of detail presented permits a good geometric visualization of the map. Errors in an earlier description of the image of the map are corrected (the complement of the image consists of two, not four, points). Techniques due to Ronen Peretz are used to verify the description of the asymptotic variety of the map.
引用
@article{arxiv.math/9812032,
title = {Picturing Pinchuk's Plane Polynomial Pair},
author = {L. Andrew Campbell},
journal= {arXiv preprint arXiv:math/9812032},
year = {2009}
}
备注
10 .tex files (ppr.tex = root); 3 encapsulated ps files (*.eps); 12 pages; originally presented 9 May 1997 at A Conference Honoring the Mathematical Work og Gary H. Meisters -- Lincoln, NB. See the following URL: http://www.math.unl.edu/Dept/Conferences/97Meisters/