A Geometric Solution to the Jacobian Problem

Abstract

In this article given a geometric solution to the well-known Jacobian problem. The twodimensionalpolynomial Keller map is considered in four-dimensional Euclidean space R4. Used the conceptof parallel. A well-known example of Vitushkin is also considered. Earlier it was known that Vitushkin’s maphas a nonzero constant Jacobian and it is not injective. We will show that the Vitushkin map is not surjectiveand moreover it has two inverse maps in the domain of its definition

Keywords

• geometric solution
• jacobian problem