Complanart of polynomial equations

Details Complanart of polynomial equations Complanart of polynomial equations

2009-07-24

arxiv.org/abs/0907.4249v2

Theor.Math.Phys.163:438-465,2010

Physics

Mathematical Physics

30 pages, 5 figures, one more particular case added

Scientific paper

10.1007/s11232-010-0034-2

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.

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