Theoretical and Mathematical Physics

, Volume 196, Issue 1, pp 957–964 | Cite as

Cartan Matrices in the Toda–Darboux Chain Theory

  • A. B. Shabat
  • V. E. Adler


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.


Cartan matrix polynomial first integral exponential system 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsChernogolovka, Moscow OblastRussia

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