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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 1, Pages 22–29
DOI: https://doi.org/10.4213/tmf9564 (Mi tmf9564) 		 
Cartan matrices in the Toda–Darboux chain theory

A. B. Shabat, V. E. Adler

Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia
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DOI: https://doi.org/10.4213/tmf9564
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.
Keywords: Cartan matrix, polynomial first integral, exponential system.
Received: 07.03.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 1, Pages 957–964
DOI: https://doi.org/10.1134/S0040577918070024
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. B. Shabat, V. E. Adler, “Cartan matrices in the Toda–Darboux chain theory”, TMF, 196:1 (2018), 22–29; Theoret. and Math. Phys., 196:1 (2018), 957–964
Citation in format AMSBIB
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