On the rational real Jacobian conjecture

Andrew Campbell

Tytuły

On the rational real Jacobian conjecture

Abstrakt

Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of Rn to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational case is proved and the Galois case clarified. Two known special cases of the Strong Real Jacobian Conjecture (SRJC) are generalized to the rational map context. For an invertible map, the associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. That disqualifies the Pinchuk counterexamples to the SRJC as candidates for invertibility.

Słowa kluczowe

Real rational map, Jacobian conjecture

Bibliografia

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Informacje

Informacje: Universitatis Iagellonicae Acta Mathematica, 2013, Tom 51, s. 7-15

Typ artykułu: Oryginalny artykuł naukowy

Tytuły:

Angielski:

On the rational real Jacobian conjecture

Polski:

On the rational real Jacobian conjecture

Autorzy

Andrew Campbell

Publikacja: 09.2014

Status artykułu: Otwarte

Licencja: Żadna

Udział procentowy autorów:

Andrew Campbell (Autor) - 100%

Korekty artykułu:

-

Języki publikacji:

Angielski

Liczba wyświetleń: 2001

Liczba pobrań: 1745

Universitatis Iagellonicae Acta Mathematica