\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\begin{thebibliography}{10}

\bibitem{BlaFerGom98Som}
H.~S. Blas~Achic, L.~A. Ferreira, J.~F. Gomes, and A.~H. Zimerman, \emph{Some
  comments on the bi(tri)-{H}amiltonian structure of generalized {A}{K}{N}{S}
  and {D}{N}{L}{S} hierarchies}, Phys. Lett. A \textbf{237} (1998), no.~4-5,
  225--233.

\bibitem{Bol91Com}
A.~V. Bolsinov, \emph{Compatible {P}oisson brackets on {L}ie algebras and the
  completeness of families of functions in involution}, Izv. Akad. Nauk SSSR
  Ser. Mat. \textbf{55} (1991), no.~1, 68--92.

\bibitem{Dam94Mul}
Pantelis~A. Damianou, \emph{Multiple {H}amiltonian structures for {T}oda-type
  systems}, J. Math. Phys. \textbf{35} (1994), no.~10, 5511--5541, Topology and
  physics.

\bibitem{DamPasSok95Tri}
Pantelis~A. Damianou, Paschalis Paschalis, and Christodoulos Sophocleous,
  \emph{A tri-{H}amiltonian formulation of the full {K}ostant-{T}oda lattice},
  Lett. Math. Phys. \textbf{34} (1995), no.~1, 17--24.

\bibitem{DeiLi91Poi}
Percy Deift and Luen~Chau Li, \emph{Poisson geometry of the analog of the
  {M}iura maps and {B}\"acklund-{D}arboux transformations for equations of
  {T}oda type and periodic {T}oda flows}, Comm. Math. Phys. \textbf{143}
  (1991), no.~1, 201--214.

\bibitem{DriSok84Alg}
V.~G. Drinfeld and V.~V. Sokolov, \emph{Lie algebras and equations of
  {K}orteweg-de {V}ries type}, Current problems in mathematics (Moscow), Itogi
  Nauki i Tekhniki, vol.~24, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn.
  Inform., 1984, pp.~81--180 (Russian).

\bibitem{FadTakh87Ham}
L.~D. Faddeev and L.~A. Takhtajan, \emph{Hamiltonian methods in the theory of
  solitons}, Springer-Verlag, Berlin, 1987, Translated from the Russian by A.
  G. Reyman [A. G. Re\u\i man].

\bibitem{FayGekh99Ele}
Leonid Faybusovich and Michael Gekhtman, \emph{Elementary {T}oda orbits and
  integrable lattices}, preprint, September 1999.

\bibitem{FerSan97Int}
Rui~L. Fernandes and Jo\~ao~P. Santos, \emph{Integrability of the periodic
  {K}{M} system}, Proceedings of the XXIX Symposium on Mathematical Physics
  (Toru\'n, 1996), vol.~40, 1997, pp.~475--484.

\bibitem{FokFuch80Str}
A.~S. Fokas and B.~Fuchssteiner, \emph{On the structure of symplectic operators
  and hereditary symmetries}, Lett. Nuovo Cimento (2) \textbf{28} (1980),
  no.~8, 299--303.

\bibitem{Gan59The}
F.~R. Gantmacher, \emph{The theory of matrices. {V}ols. 1, 2}, Chelsea
  Publishing Co., New York, 1959, Translated by K. A. Hirsch.

\bibitem{GekhShap99Non}
M.~I. Gekhtman and M.~Z. Shapiro, \emph{Noncommutative and commutative
  integrability of generic {T}oda flows in simple {L}ie algebras}, Comm. Pure
  Appl. Math. \textbf{52} (1999), no.~1, 53--84.

\bibitem{GelDor79Ham}
I.~M. Gel{\cprime}fand and I.~Ja. Dorfman, \emph{Hamiltonian operators and
  algebraic structures associated with them}, Funktsional. Anal. i Prilozhen.
  \textbf{13} (1979), no.~4, 13--30, 96.

\bibitem{GelZakhFAN}
Israel~M. Gelfand and Ilya Zakharevich, \emph{Spectral theory for a pair of
  skew-symmetrical operators on {$ S^1 $}}, Func. Anal. Appl. \textbf{23}
  (1989), no.~1, 85--93.

\bibitem{GelZakhWeb}
\bysame, \emph{Webs, {V}eronese curves, and bihamiltonian systems}, J. of Func.
  Anal. \textbf{99} (1991), 150--178.

\bibitem{GelZakh93}
\bysame, \emph{On the local geometry of bihamiltonian structures}, The Gelfand
  mathematical seminar, 1990--1992 (Boston), Birkh\"auser, 1993, pp.~51--112.

\bibitem{GelZakh94Spe}
\bysame, \emph{The spectral theory for a pencil of skewsymmetrical differential
  operators of the third order}, Comm. Pure Appl. Math. \textbf{47} (1994),
  no.~8, 1031--1041.

\bibitem{Kacvan75Exp}
M.~Kac and Pierre van Moerbeke, \emph{On an explicitly soluble system of
  nonlinear differential equations related to certain {T}oda lattices},
  Advances in Math. \textbf{16} (1975), 160--169.

\bibitem{Kir76Loc}
A.~A. Kirillov, \emph{Local {L}ie algebras}, Uspehi Mat. Nauk \textbf{31}
  (1976), no.~4(190), 57--76.

\bibitem{KosMag96Lax}
Y.~Kosmann-Schwarzbach and F.~Magri, \emph{Lax-{N}ijenhuis operators for
  integrable systems}, J. Math. Phys. \textbf{37} (1996), no.~12, 6173--6197.

\bibitem{Kos79Sol}
Bertram Kostant, \emph{The solution to a generalized {T}oda lattice and
  representation theory}, Adv. in Math. \textbf{34} (1979), no.~3, 195--338.

\bibitem{Lax76Alm}
Peter~D. Lax, \emph{Almost periodic solutions of the {K}d{V} equation}, SIAM
  Rev. \textbf{18} (1976), no.~3, 351--375.

\bibitem{Lev87Inv}
B.~M. Levitan, \emph{Inverse {S}turm-{L}iouville problems}, VSP, Zeist, 1987,
  Translated from the Russian by O. Efimov.

\bibitem{Mag78Sim}
Franco Magri, \emph{A simple model of the integrable {H}amiltonian equation},
  Journal of Mathematical Physics \textbf{19} (1978), no.~5, 1156--1162.

\bibitem{Mag88Geo}
\bysame, \emph{On the geometry of soliton equations}, Preprint, 1988.

\bibitem{Mag95Geo}
\bysame, \emph{On the geometry of soliton equations}, Acta Appl. Math.
  \textbf{41} (1995), no.~1-3, 247--270, Geometric and algebraic structures in
  differential equations.

\bibitem{McKeanPC}
Henri McKean, private communication, 1990.

\bibitem{MorPiz96Eul}
Carlo Morosi and Livio Pizzocchero, \emph{On the {E}uler equation:
  bi-{H}amiltonian structure and integrals in involution}, Lett. Math. Phys.
  \textbf{37} (1996), no.~2, 117--135.

\bibitem{OlvRos96Tri}
Peter~J. Olver and Philip Rosenau, \emph{Tri-{H}amiltonian duality between
  solitons and solitary-wave solutions having compact support}, Phys. Rev. E
  (3) \textbf{53} (1996), no.~2, 1900--1906.

\bibitem{Pan99Ver}
Andriy Panasyuk, \emph{Veronese webs for bihamiltonian structures of higher
  corank}, {B}anach {C}enter {P}ublications, {P}oisson geometry, {P}roceedings
  of the conference dedicated to the memory of {S}tanislaw {Z}akrzewski, Warsaw
  1998 (Warszawa) (Pawel Urba\'{n}ski and Janusz Grabowski, eds.), {I}nstytut
  {M}atematyczny {PAN}, 1999, to appear.

\bibitem{Rig95Tis}
Marie-H{\'e}l{\`e}ne Rigal, \emph{Tissus de {V}\'eron\`ese en dimension 3},
  S\'eminaire Gaston Darboux de G\'eom\'etrie et Topologie Diff\'erentielle,
  1994--1995 (Montpellier), Univ. Montpellier II, Montpellier, 1995, pp.~iv,
  63--68.

\bibitem{Rig98Sys}
\bysame, \emph{Syst\`emes bihamiltoniens en dimension impaire}, Ann. Sci.
  \'Ecole Norm. Sup. (4) \textbf{31} (1998), no.~3, 345--359.

\bibitem{Ruj90Rel}
S.~N.~M. Ruijsenaars, \emph{Relativistic {T}oda systems}, Comm. Math. Phys.
  \textbf{133} (1990), no.~2, 217--247.

\bibitem{Thom91Pen}
Robert~C. Thompson, \emph{Pencils of complex and real symmetric and skew
  matrices}, Linear Algebra Appl. \textbf{147} (1991), 323--371.

\bibitem{TsuTakKaj97Tri}
Takayuki Tsuchida, Yasumasa Kajinaga, and Miki Wadati, \emph{Tri-{H}amiltonian
  structure and complete integrability of {V}olterra model}, J. Phys. Soc.
  Japan \textbf{66} (1997), no.~9, 2608--2617.

\bibitem{Tur89Cla}
Francisco-Javier Turiel, \emph{Classification locale d'un couple de formes
  symplectiques {P}oisson-compatibles}, Comptes Rendus des Seances de
  l'Academie des Sciences. Serie I. Mathematique \textbf{308} (1989), no.~20,
  575--578.

\bibitem{Tur99Equi}
\bysame, \emph{${C}\sp \infty$-\'equivalence entre tissus de {V}eronese et
  structures bihamiltoniennes}, C. R. Acad. Sci. Paris S\'er. I Math.
  \textbf{328} (1999), no.~10, 891--894.

\bibitem{TurAith61Int}
H.~W. Turnbull and A.~C. Aitken, \emph{An introduction to the theory of
  canonical matrices}, Dover Publications Inc., New York, 1961.

\bibitem{Wei83Loc}
Alan Weinstein, \emph{The local structure of {P}oisson manifolds}, J.
  Differential Geom. \textbf{18} (1983), no.~3, 523--557.

\bibitem{Zakh99Kro}
Ilya Zakharevich, \emph{Kronecker webs, bihamiltonian structures, and the
  method of argument translation}, Archived as math.SG/9908034.

\end{thebibliography}