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Abstract
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We construct integrable and superintegrable Hamiltonian systems using the realizations
of four dimensional real Lie algebras as a symmetry of the system with the
phase space R4 and R6. Furthermore, we construct some integrable and superintegrable
Hamiltonian systems for which the symmetry Lie group is also the phase space
of the system. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4875155]
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