Regular analytic transformations of $ℝ^2$

• Autorzy: Joseph Gubeladze
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

injectivity; regular analytic maps; Jacobian

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 2
• Strony: 99-109

Daty

wydano

2000

otrzymano

1999-02-05

poprawiono

2000-05-31

Twórcy

autor

Joseph Gubeladze

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

Bibliografia

• [BR] A. Białynicki-Birula and M. Rosenlicht, Injective morphisms of real algebraic varieties, Proc. Amer. Math. Soc. 13 (1962), 200-204.
• [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.
• [KR] K. Kurdyka and K. Rusek, Polynomial rational bijections of $ℝ^n$, Proc. Amer. Math. Soc. 112 (1988), 804-808.
• [P] S. Pinchuk, A counterexample to the strong real Jacobian conjecture, Math. Z. 217 (1994), 1-4.