Functions from $R^2$ to $R^2$: a study in nonlinearity
Numerical Analysis
2025-10-20 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@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}
}
Comments
24 pages, 15 figures Completely rewritten to make it more elementary