  Commuting pairs of ordinary differential operators are classified by a set of
algebro-geometric data called ``algebraic spectral data''. These data consist
of an algebraic curve (``spectral curve'') $\Gamma$ with a marked point
$\gamma_\infty$, a holomorphic vector bundle $E$ on $\Gamma$ and some
additional data related to the local structure of $\Gamma$ and $E$ in a
neighborhood of $\gamma_\infty$. If the rank $r$ of $E$ is greater than 1, one
can use the so called ``Tyurin parameters'' in place of $E$ itself. The Tyurin
parameters specify the pole structure of a basis of joint eigenfunctions of the
commuting pair. These data can be translated to the language of an infinite
dimensional Grassmann manifold. This leads to a dynamical system of the
standard exponential flows on the Grassmann manifold, in which the role of
Tyurin parameters and some other parameters is made clear.
