Nucci, M. C.Campoamor Stursberg, Otto-Rudwig2023-06-172023-06-172021-01-250022-248810.1063/5.0007377https://hdl.handle.net/20.500.14352/7290All maximally superintegrable Hamiltonian systems in three-dimensional flat space derived in the work of Evans [Phys. Rev. A 41, 5666–5676 (1990)] are shown to possess hidden symmetries leading to their linearization, likewise the maximally superintegrable Hamiltonian systems in two-dimensional flat space as shown in the work of Gubbiotti and Nucci [J. Math. Phys. 58, 012902 (2017)]. We conjecture that even minimally superintegrable systems in three-dimensional flat space have hidden symmetries that make them linearizable.engjournal articlehttps://doi.org/10.1063/5.0007377open access512Hamilton-Jacobi equationsHamiltonian mechanicsSymmetry algebraGroup analysis approachLie algebrasÁlgebra1201 Álgebra