# Regular analytic transformations of ${\mathbb{R}}^{2}$

Annales Polonici Mathematici (2000)

- Volume: 75, Issue: 2, page 99-109
- ISSN: 0066-2216

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topGubeladze, Joseph. "Regular analytic transformations of $ℝ^2$." Annales Polonici Mathematici 75.2 (2000): 99-109. <http://eudml.org/doc/208394>.

@article{Gubeladze2000,

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.},

author = {Gubeladze, Joseph},

journal = {Annales Polonici Mathematici},

keywords = {injectivity; regular analytic maps; Jacobian; analytic mapping; jacobian conjecture},

language = {eng},

number = {2},

pages = {99-109},

title = {Regular analytic transformations of $ℝ^2$},

url = {http://eudml.org/doc/208394},

volume = {75},

year = {2000},

}

TY - JOUR

AU - Gubeladze, Joseph

TI - Regular analytic transformations of $ℝ^2$

JO - Annales Polonici Mathematici

PY - 2000

VL - 75

IS - 2

SP - 99

EP - 109

AB - 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.

LA - eng

KW - injectivity; regular analytic maps; Jacobian; analytic mapping; jacobian conjecture

UR - http://eudml.org/doc/208394

ER -

## References

top- [BR] A. Białynicki-Birula and M. Rosenlicht, Injective morphisms of real algebraic varieties, Proc. Amer. Math. Soc. 13 (1962), 200-204. Zbl0107.14602
- [F] W. Fulton, Algebraic Topology (a First Course), Grad. Texts in Math. 153, Springer, 1995.
- [Gw] J. Gwoździewicz, The Real Jacobian Conjecture for polynomials of degree 3, preprint, 1999.
- [Ha] J. Hadamard, Sur les transformations ponctuelles, Bull. Soc. Math. France 34 (1906), 71-84. Zbl37.0672.02
- [KR] K. Kurdyka and K. Rusek, Polynomial rational bijections of ${\mathbb{R}}^{n}$, Proc. Amer. Math. Soc. 112 (1988), 804-808. Zbl0718.13006
- [P] S. Pinchuk, A counterexample to the strong real Jacobian conjecture, Math. Z. 217 (1994), 1-4. Zbl0874.26008

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