Cartan Matrices in the Toda–Darboux Chain Theory
- 29 Downloads
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
Unable to display preview. Download preview PDF.
- 4.A. Shabat and R. Yamilov, “Exponential systems of type I and Cartan matrices [in Russian],” Preprint Bashkir Affiliate, Acad. Sci. USSR, BFAN USSR, Ufa (1981).Google Scholar
- 5.A. N. Leznov and A. B. Shabat, “Truncation conditions of perturbation theory series [in Russian],” in: Integrable Systems (A. B. Shabat, ed.), BFAN USSR, Ufa (1982), pp. 34–44.Google Scholar