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Evolutionary method of construction of solutions of polynomials and related generalized dynamics. (English) Zbl 1239.12007

Summary: Invariant theory as a study of properties of polynomials under translational transformations is developed. A class of polynomials with congruent set of eigenvalues is introduced. Evolution equations for eigenvalues and coefficients are formulated such that the polynomials remain within a proper class of polynomials. The connection with equations for hyper-elliptic Weierstrass and hyper-elliptic Jacobian functions is found. An algorithm for the calculation of eigenvalues of the polynomials based on the evolution process is elaborated. Elements of the generalized dynamics with \(n\)-order characteristic polynomials are built.

MSC:

12Y05 Computational aspects of field theory and polynomials (MSC2010)
34A05 Explicit solutions, first integrals of ordinary differential equations
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