Borisov, A. V.; Mamaev, I. S. Necessary and sufficient conditions for polynomial integrability of generalized Toda chains. (Russian) Zbl 1049.68097 Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 4, 449-453 (2004). The authors prove a condition, which makes it possible to describe, in terms of Dynkin diagrams, spectra of generalized Toda chains. These chains satisfy necessary conditions of integrability according to Birkhoff. Classification of Dynkin’s diagrams and corresponding irreducible integrable chains are presented. The first integrals and L-A pairs are analyzed. Reviewer: Andrei Zemskov (Moskva) Cited in 2 Documents MSC: 68R10 Graph theory (including graph drawing) in computer science Keywords:Hamiltonian; Toda chain; Birkhoff integrability; Dynkin’s diagrams; Coxeter graphs PDFBibTeX XMLCite \textit{A. V. Borisov} and \textit{I. S. Mamaev}, Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 4, 449--453 (2004; Zbl 1049.68097)