Regular analytic transformations of $ℝ^2$

Joseph Gubeladze

ArticleOriginal scientific text

Title

Regular analytic transformations of $ℝ^{2}$

Authors ¹

Affiliations

A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Alexidze Str. 1, Tbilisi 380093, Republic of Georgia

Abstract

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.

Keywords

ENG

injectivity, regular analytic maps, Jacobian

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Title

Regular analytic transformations of ℝ2

Affiliations

Abstract

Keywords

Bibliography

Regular analytic transformations of $ℝ^{2}$