Functions from $R^2$ to $R^2$: a study in nonlinearity

Details Functions from $R^2$ to $R^2$: a study in nonlinearity Functions from $R^2$ to $R^2$: a study in nonlinearity

2002-09-09

arxiv.org/abs/math/0209097v2

Mathematics

Numerical Analysis

24 pages, 15 figures Completely rewritten to make it more elementary

Scientific paper

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.

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