  In this paper we consider Hamiltonian systems on the quantum plane and we
show that the set of Q-meromorphic Hamiltonians is a Virasoro algebra with
central charge zero and the set of Hamiltonian derivations of the algebra of
$Q$-analytic functions ${\cal A}_q$ with values in the algebra of
$Q$-meromorphic functions ${\cal M}_q$ is the Lie algebra $sl(2,A_1(q)).$
Moreover we will show that any motion on a quantum space is associated with a
quadratic Hamiltonian.
