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Monodromy, differential equations and the Jacobian conjecture

100%

Friedland S.

Annales Polonici Mathematici

1999

tom 72

nr 3

219-249

We study certain problems on polynomial mappings related to the Jacobian conjecture.

Non-zero constant Jacobian polynomial maps of $ℂ²$

100%

Chau N.

Annales Polonici Mathematici

1999

tom 71

nr 3

287-310

We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.

A characterization of p-bases of rings of constants

100%

Jędrzejewicz P.

Open Mathematics

2013

tom 11

nr 5

900-909

We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Open Mathematics

1 Chau N.

1 Friedland S.

1 Jędrzejewicz P.

1 2013

2 1999

Wyniki wyszukiwania

Monodromy, differential equations and the Jacobian conjecture

Non-zero constant Jacobian polynomial maps of $ℂ²$

A characterization of p-bases of rings of constants