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- W2164841723 abstract "Ž . where H s H , . . . , H and each H is either zero or a homogeneous 1 n i Ž . polynomial map of degree 3. In this case the Jacobian condition det JF g U Ž C is equivalent to JH is nilpotent. JF and JH are the Jacobian matrices . of F and H. So understanding nilpotent Jacobian matrices is crucial in w x the study of the Jacobian Conjecture. In 14 Wright showed that if n s 3 w x all JH where H is cubic homogeneous are linearly triangularizable. In 10 the second author gave a complete description of all cubic homogeneous Jacobian matrices in case n s 4. They are no longer linearly triangularizable. However, it turns out that the rows of the Jacobian matrices are Ž linearly dependent over C or equivalently that H H , H , and H 1 2 3 4 . w x linearly dependent over C . Already in 4 Druzkowski and Rusek conjec tured that if H s l , . . . , H s l , where each l is a linear form, then the 1 1 n n i nilpotence of JH implies the linear dependence of H , . . . , H . The same 1 n w x question of linear dependence of H , . . . , H was raised by Olech in 13 1 n w x and Meisters in 12 , in case H , . . . , H are cubic homogeneous. 1 n" @default.
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- W2164841723 date "1997-01-01" @default.
- W2164841723 modified "2023-09-26" @default.
- W2164841723 title "A new class of invertible polynomial maps" @default.
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