Generic Kronecker conjecture for Volterra, Toda, Euler-top, and regular Lie-coalgebra systems
The odd-dimensional open Volterra system, the even-dimensional periodic Volterra system, the full Toda lattice, the multidimensional Euler top, and the regular case of the cited bihamiltonian Lie-coalgebra example are bihamiltonian systems. Generic Kronecker conjecture. These systems are generically Kronecker bihamiltonian structures. The paper notes that the part concerning the regular Lie-coalgebra example was proved in the cited work by Zakharevich, while the remaining cases are not established here.
References
Primary source
Israel M. Gelfand and Ilya Zakharevich, “Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures”, arXiv:math/9903080 (2000).
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