On cubic-linear polynomial mappings |
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Authors: | Gianluca Gorni Gaetano Zampieri |
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Institution: | aUniversità di Udine, Dipartimento di Matematica e Informatica, via delle Scienze 208, 33100 Udine, Italy;bDipartimento di Matematica, via Carlo Alberto 10,10123 Torino, Italy |
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Abstract: | In the field of the Jacobian conjecture it is well-known after Dru?kowski that from a polynomial ‘cubic-homogeneous’ mapping we can build a higher-dimensional ‘cubic-linear’ mapping and the other way round, so that one of them is invertible if and only if the other one is. We make this point clearer through the concept of ‘pairing’ and apply it to the related conjugability problem: one of the two maps is conjugable if and only if the other one is; moreover, we find simple formulas expressing the inverse or the conjugations of one in terms of the inverse or conjugations of the other. Two nontrivial examples of conjugable cubic-linear mappings are provided as an application. |
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