An example of non-Keller mapping

Abstract

Abstract. In the paper a nontrivial example of non-Keller mapping is considered. It is shown that the Jacobian of rare mapping, having one zero at infinity, being constant must vanish.

The non-Keller mapping with one zero at infinity

“…In [1,2] the rare mappings with one zero at infinity was analyzed. It is shown that the Jacobian of non-Keller mapping being constant must vanish.…”

The Jacobians of non-maximal degree

“…The Jacobians Conjecture [4][5][6][7][8][9] do not occur for non trivial classes of the mappings having the constant Jacobian and one or two zeros in infinity [3,10]. In the second case (two zeros in infinity) the leading forms of the mapping have the form given in the Corollary 2.…”