Optimal phase-covariant cloning for qubits and qutrits

We consider cloning transformations of equatorial qubits |ψ_φ>=1/(2)(|0>+e^iφ|1>) and qutrits |ψ_φ,θ>=1/(3)(|0>+e^iφ|1>+e^iθ|2>), with the transformation covariant for rotation of the phases φ and θ. The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.