The Jacobian conjecture: structure of Keller mappings

The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping $f: \Bbb R^n \to \Bbb R^n$ ($\Bbb C^n \to \Bbb C^n$) under the assumption that $J_f\equiv const\ne0$. In this paper, we consider the structure of polynomial mappings $f$ with $J_f\equiv const \ne0$.