Rodríguez González, Miguel ÁngelTempesta, Piergiulio2023-06-222023-06-222022-12-161751-811310.1088/1751-8121/acaadahttps://hdl.handle.net/20.500.14352/72911© 2022 IOP Publishing Ltd. We wish to thank G Gubbiotti and D Latini for interesting discussions. This work has been partly supported by the Universidad Complutense de Madrid under Grant G/6400100/3000, and by the Severo Ochoa Programme for Centres of Excellence in R & D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades y Agencia Estatal de Investigacion, Spain.P T is member of the Gruppo Nazionale di Fisica Matematica (GNFM).We introduce a family of n-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic oscillator with Rosochatius terms. We conjecture that there exist special values in the space of parameters, apart from those leading to known cases, for which this new Hamiltonian family is superintegrable.engjournal articlehttp://dx.doi.org/10.1088/1751-8121/acaadahttps://iopscience.iop.org/open access51-73Exact solvabilitySymmetries.Física-Modelos matemáticosFísica matemática