  The Davey-Stewartson I equation is a typical integrable equation in 2+1
dimensions. Its Lax system being essentially in 1+1 dimensional form has been
found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the
present paper, this essentially 1+1 dimensional Lax system is further
nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann
constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems
are completely integrable in Liouville sense by finding a full set of integrals
of motion and proving their functional independence.
