Cartan Matrices in the Toda–Darboux Chain Theory
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We discuss a one-to-one correspondence between the polynomial first integrals of Hamiltonian systems with exponential interaction and the hyperintegrals of the two-dimensional Toda lattice. We establish formulas for recalculating the corresponding polynomials and some general properties of their algebraic structure.
KeywordsCartan matrix polynomial first integral exponential system
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