  We study the discrete and continuous versions of the Markus- Yamabe
Conjecture for polynomial vector fields in R^n (especially when n = 3) of the
form X = \lambda I+H where \lambda is a real number, I the identity map, and H
a map with nilpotent Jacobian matrix JH. We consider the case where the rows of
JH are linearly dependent over R and that where they are linearly independent
over R. In the former, we find non-linearly triangularizable vector fields X
for which the origin is a global attractor for both the continuous and the
discrete dynamical systems generated by X. In the independent continuous case,
we present a family of vector fields which have orbits escaping to infinity. In
the independent discrete case, we present a large family of vector fields which
have a periodic point of period 3.
