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Regular analytic transformations of $ℝ^{2}$

Joseph Gubeladze — 2000

Annales Polonici Mathematici

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.