Díaz-Cano Ocaña, AntonioGonzalez Gascón, F.2023-06-202023-06-2020101468-936710.1080/14689361003761959https://hdl.handle.net/20.500.14352/42136The frontiers of boundedness F(b) of the orbits of dynamical systems X defined on R(n) are studied. When X is completely integrable some topological properties of F(b) are found and, in certain cases, F(b) is localized with the help of symmetries of X. Several examples in dimensions 2 and 3 are provided. In case the number of known first integrals of the vector field X is less than n - 1, an interesting connection of F(b) with the frontier of boundedness of the level-sets of the first integrals of X is proved. This result also applies to Hamiltonian systems.engjournal articlehttp://www.tandfonline.com/doi/pdf/10.1080/14689361003761959http://www.tandfonline.com/loi/cdss20restricted access517.9Dynamical systemsFrontierFirst integralSymmetriesEcuaciones diferenciales1202.07 Ecuaciones en Diferencias