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oai:docta.ucm.es:20.500.14352/421362023-08-27T22:09:28Zcom_20.500.14352_14col_20.500.14352_15

Frontiers and symmetries of dynamical systems Díaz-Cano Ocaña, Antonio Gonzalez Gascón, F. 517.9 Dynamical systems Frontier First integral Symmetries Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias The 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. GAAR Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-20T00:10:42Z 2023-06-20T00:10:42Z 2010 journal article https://hdl.handle.net/20.500.14352/42136 1468-9367 10.1080/14689361003761959 eng MTM2008-00272 Grupos UCM 910444. restricted access application/pdf Taylor & Francis