A continuum of Hamiltonian structures for the two-dimensional isotropic   harmonic oscillator
  We show the existence of a continuum of Hamiltonian structures for the two-dimensional isotropic harmonic oscillator. In particular, a continuum of Hamiltonian structures having noncommutative coordinates is presented. A study of the symmetries of these structures is performed and their physical plausibility is discussed. 
Juan M. Romero and Adolfo Zamora