Regular analytic transformations of ℝ 2

Joseph Gubeladze

Annales Polonici Mathematici (2000)

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

Abstract

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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.

How to cite

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Gubeladze, 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

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

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