Geodesic
Regular analytic transformations of $ℝ^2$
Annales Polonici Mathematici, Tome 75 (2000) no. 2, pp. 99-109 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 1

1 
@article{10_4064_ap_75_2_99_109,
     author = {Joseph Gubeladze},
     title = {Regular analytic transformations of $\ensuremath{\mathbb{R}}^2$},
     journal = {Annales Polonici Mathematici},
     pages = {99--109},
     year = {2000},
     volume = {75},
     number = {2},
     doi = {10.4064/ap-75-2-99-109},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-75-2-99-109/}
}
TY  - JOUR
AU  - Joseph Gubeladze
TI  - Regular analytic transformations of $ℝ^2$
JO  - Annales Polonici Mathematici
PY  - 2000
SP  - 99
EP  - 109
VL  - 75
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-75-2-99-109/
DO  - 10.4064/ap-75-2-99-109
LA  - en
ID  - 10_4064_ap_75_2_99_109
ER  - 
%0 Journal Article
%A Joseph Gubeladze
%T Regular analytic transformations of $ℝ^2$
%J Annales Polonici Mathematici
%D 2000
%P 99-109
%V 75
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-75-2-99-109/
%R 10.4064/ap-75-2-99-109
%G en
%F 10_4064_ap_75_2_99_109
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

Cité par Sources :