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Herranz","submitted_at":"2012-06-30T10:13:27Z","abstract_excerpt":"An integrable generalization on the two-dimensional sphere S^2 and the hyperbolic plane H^2 of the Euclidean anisotropic oscillator Hamiltonian with \"centrifugal\" terms given by $H=1/2(p_1^2+p_2^2)+ \\delta q_1^2+(\\delta + \\Omega)q_2^2 +\\frac{\\lambda_1}{q_1^2}+\\frac{\\lambda_2}{q_2^2}$ is presented. The resulting generalized Hamiltonian H_\\kappa\\ depends explicitly on the constant Gaussian curvature \\kappa\\ of the underlying space, in such a way that all the results here presented hold simultaneously for S^2 (\\kappa>0), H^2 (\\kappa<0) and E^2 (\\kappa=0). 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