Complanart of system of polynomial equations
نویسنده
چکیده
In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. 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 de nes the phase diagram of associated di erential equation żi = Ai1i2···is i zi1zi2zi3 · · · zis . Theory of such di erential equations arise naturally as extension of Lyapunov's theory of stability for solutions of di erential equations. The results of this work have a number of potential applications: from solving non-linear di erential equations and calculating non-linear exponents to taking non-Gaussian integrals.
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