Geodesic
Regular analytic transformations of $ℝ^2$
Annales Polonici Mathematici, Tome 75 (2000) no. 2, pp. 99-109

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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 $ℝ^2$ 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.
DOI : 10.4064/ap-75-2-99-109
Keywords: injectivity, regular analytic maps, Jacobian 
Joseph Gubeladze. Regular analytic transformations of $ℝ^2$. Annales Polonici Mathematici, Tome 75 (2000) no. 2, pp. 99-109. doi: 10.4064/ap-75-2-99-109
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