Yamaleev, Robert M. Evolutionary method of construction of solutions of polynomials and related generalized dynamics. (English) Zbl 1239.12007 Cubo 13, No. 1, 25-43 (2011). 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 PDFBibTeX XMLCite \textit{R. M. Yamaleev}, Cubo 13, No. 1, 25--43 (2011; Zbl 1239.12007) Full Text: DOI