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Frontiers and symmetries of dynamical systems

Díaz-Cano Ocaña, Antonio and Gonzalez Gascón, F. (2010) Frontiers and symmetries of dynamical systems. Dynamical Systems: An International Journal, 25 (4). pp. 501-518. ISSN 1468-9367

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Dynamical systems; Frontier; First integral; Symmetries
Subjects:Sciences > Mathematics > Differential equations
ID Code:14984
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