Multiple Hamiltonian Structures for Toda Systems of Type $A-B-C$

Results on the finite nonperiodic $A_n$ Toda lattice are extended to the Bogoyavlensky–Toda systems of type $B_n$ and $C_n$. The investigated areas include master symmetries, recursion operators, higher Poisson brackets and invariants. A conjecture which relates the degrees of higher Poisson brackets and the exponents of the corresponding Lie group is verified for these systems.