Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.
@article{bwmeta1.element.bwnjournal-article-apmv75z2p99bwm,
author = {Gubeladze, Joseph},
title = {Regular analytic transformations of $$\mathbb{R}$^2$
},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {99-109},
zbl = {0964.14048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv75z2p99bwm}
}
Gubeladze, Joseph. Regular analytic transformations of $ℝ^2$
. Annales Polonici Mathematici, Tome 75 (2000) pp. 99-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z2p99bwm/
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