The class of the cubic-homogenous mappings with nonzero constant Jacobian determinant is interesting because if it were proved that all mappings in this class are invertible, then the general Jacobian Conjecture would follow. A secondary conjecture was that all mappings in this class had linear invariants. De Bondt has recently put that to rest, with an example that has no linear invariants. Still, de Bondt's mapping has quadratic invariants. In this paper we exhibit an example in dimension 11 that has a cubic invariant but no quadratic (or linear) ones.
Search for homogeneous polynomial invariants and a cubic-homogeneous mapping without quadratic invariants
ZAMPIERI, Gaetano
2008-01-01
Abstract
The class of the cubic-homogenous mappings with nonzero constant Jacobian determinant is interesting because if it were proved that all mappings in this class are invertible, then the general Jacobian Conjecture would follow. A secondary conjecture was that all mappings in this class had linear invariants. De Bondt has recently put that to rest, with an example that has no linear invariants. Still, de Bondt's mapping has quadratic invariants. In this paper we exhibit an example in dimension 11 that has a cubic invariant but no quadratic (or linear) ones.File in questo prodotto:
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