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Cartan Matrices in the Toda–Darboux Chain Theory

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Abstract

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.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

    A. B. Shabat & V. E. Adler

Authors
  1. A. B. Shabat
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  2. V. E. Adler
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Correspondence to A. B. Shabat.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 196, No. 1, pp. 22–29, July, 2018.

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Shabat, A.B., Adler, V.E. Cartan Matrices in the Toda–Darboux Chain Theory. Theor Math Phys 196, 957–964 (2018). https://doi.org/10.1134/S0040577918070024

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  • DOI: https://doi.org/10.1134/S0040577918070024

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