  We consider the most general scale invariant radial Hamiltonian allowing for
anisotropic scaling between space and time. We formulate a renormalisation
group analysis of this system and demonstrate the existence of a quantum phase
transition from a continuous scale invariant phase to a discrete scale
invariant phase. Close to the critical point, the discrete scale invariant
phase is characterised by an isolated, closed, attracting trajectory in
renomalisation group space (a limit cycle). Moving in appropriate directions in
the parameter space of couplings this picture is altered to one controlled by a
quasi periodic attracting trajectory (a limit torus) or fixed points. We
identify a direct relation between the critical point, the renormalisation
group picture and the power laws characterising the zero energy wave functions.
