The dynamical behavior of the rational vectorial operator associated
with a multidimensional iterative method in polynomial systems, gives us
interesting information about the stability of the iterative scheme. The
stability of fixed points, dynamic planes, bifurcation diagrams, etc.
are known tools that act in this sense. In this manuscript, we introduce
a new tool, which we call isonormal surface, to complement the
information about the stability of the iterative method provided by the
dynamic elements mentioned above. These dynamical instruments are used
for analyze the stability of a parametric family of multidimensional
iterative schemes in terms of the value of the parameter. Some numerical
tests confirm the obtained dynamical results.