The paper raises two problems on the homogeneous polynomial invariants for the cubic-homogeneous functions with constant Jacobian determinant. These last functions are sufficient to study the Jacobian conjecture. The questions hopefully permit to deepen the research on the line of the linear dependence problem recently solved by a counterexample found by de Bondt in dimension 10. The paper also gives a variant of de Bondt's example in dimension 9.
Homogeneous polynomial invariants for cubic-homogeneous functions
ZAMPIERI, Gaetano
2008-01-01
Abstract
The paper raises two problems on the homogeneous polynomial invariants for the cubic-homogeneous functions with constant Jacobian determinant. These last functions are sufficient to study the Jacobian conjecture. The questions hopefully permit to deepen the research on the line of the linear dependence problem recently solved by a counterexample found by de Bondt in dimension 10. The paper also gives a variant of de Bondt's example in dimension 9.
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