Regular analytic transformations of $ℝ^2$
Tom 75 / 2000
Annales Polonici Mathematici 75 (2000), 99-109 DOI: 10.4064/ap-75-2-99-109
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.