Authors: Dhananjay P. Mehendale
The so called Jacobian problem [1] or Jacobian conjecture [2], [3] demands the existence of inverse functions of polynomial nature when the Jacobian is a nonzero constant (=1). Bass, Connell, Wright in there paper [3] have shown that it is enough to construct (or show the existence of) such inverse polynomials for special type of cubic polynomials whose Jacobian is a nonzero constant (=1).To settle Jacobian conjecture one needs to show the existence of inverse polynomials for special type of cubic polynomials whose Jacobian is a nonzero constant (=1) for all dimensions [3]. In this paper we explicitly give these inverse polynomials for two and three dimensions, i.e. for two and three variables cases. Any higher dimensional cases are no different than these special cases and it is possible to obtain such inverse polynomials in any higher dimensional cases also.
Comments: 22 Pages
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[v1] 2016-10-11 23:26:02
[v2] 2016-10-20 23:29:55
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