MathDBGeneric Kronecker conjecture for Volterra, Toda, Euler-top, and regular Lie-coalgebra systems
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.
Sources & referencesView supporting material
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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