Functions from $R^2$ to $R^2$: a study in nonlinearity
数值分析
2025-10-20 v2 数值分析
摘要
We study the geometry of functions from the plane to the plane. For a large special class we are able to count preimages and compute them. Both numerical and theoretical aspects are discussed. Some of the tools used are Whitney's classification of critical points, rotation numbers, covering maps and continuation methods.
引用
@article{arxiv.math/0209097,
title = {Functions from $R^2$ to $R^2$: a study in nonlinearity},
author = {Nicolau C. Saldanha and Carlos Tomei},
journal= {arXiv preprint arXiv:math/0209097},
year = {2025}
}
备注
24 pages, 15 figures Completely rewritten to make it more elementary