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The SL(2,R) invariant Hamiltonian systems are discussed within the framework of the orbit method. It is shown that both the dynamics and the symmetry transformations are globally well-defined on phase space. The flexibility in the choice of the time variable and the Hamiltonian function described in the paper by de Alfaro et al. [Nuovo Cimento 34A (1976) 569] is related to the nontrivial global structure of 1+0-dimensional space–time. The operational definition of time is discussed.