  In this paper we study polynomial maps of vector spaces and their
eigenvectors and eigenvalues. The new quantity called complanart is defined.
Complanarts determine complanarity of solution vectors of systems of polynomial
equations. Evaluation of complanart is reduced to evaluation of resultants. As
in linear case, the pattern of eigenvectors defines the phase diagram of
associated differential equation. Theory of such differential equations arise
naturally as extension of Lyapunov's theory of stability for solutions of
differential equations. The results of this work have a number of potential
applications: from solving non-linear differential equations and calculating
non-linear exponents to taking non-Gaussian integrals.
